Communications in Contemporary Mathematics最新文献

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Moduli spaces of ℤ/kℤ-constellations over 𝔸2 ℤ/kℤ-constellations over 𝔸2 的模空间
IF 1.6 2区 数学
Communications in Contemporary Mathematics Pub Date : 2024-04-10 DOI: 10.1142/s0219199724500196
Michele Graffeo
{"title":"Moduli spaces of ℤ/kℤ-constellations over 𝔸2","authors":"Michele Graffeo","doi":"10.1142/s0219199724500196","DOIUrl":"https://doi.org/10.1142/s0219199724500196","url":null,"abstract":"","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140717597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sharp spectral gap estimates for higher-order operators on Cartan–Hadamard manifolds Cartan-Hadamard 流形上高阶算子的尖锐谱差距估计值
IF 1.6 2区 数学
Communications in Contemporary Mathematics Pub Date : 2024-04-10 DOI: 10.1142/s0219199724500135
Csaba Farkas, Sándor Kajántó, Alexandru Kristály
{"title":"Sharp spectral gap estimates for higher-order operators on Cartan–Hadamard manifolds","authors":"Csaba Farkas, Sándor Kajántó, Alexandru Kristály","doi":"10.1142/s0219199724500135","DOIUrl":"https://doi.org/10.1142/s0219199724500135","url":null,"abstract":"<p>The goal of this paper is to provide sharp spectral gap estimates for problems involving higher-order operators (including both the clamped and buckling plate problems) on Cartan–Hadamard manifolds. The proofs are symmetrization-free — thus no sharp isoperimetric inequality is needed — based on two general, yet elementary functional inequalities. The spectral gap estimate for clamped plates solves a sharp asymptotic problem from [Q.-M. Cheng and H. Yang, Universal inequalities for eigenvalues of a clamped plate problem on a hyperbolic space, <i>Proc. Amer. Math. Soc.</i><b>139</b>(2) (2011) 461–471] concerning the behavior of higher-order eigenvalues on hyperbolic spaces, and answers a question raised in [A. Kristály, Fundamental tones of clamped plates in nonpositively curved spaces, <i>Adv. Math.</i><b>367</b>(39) (2020) 107113] on the validity of such sharp estimates in high-dimensional Cartan–Hadamard manifolds. As a byproduct of the general functional inequalities, various Rellich inequalities are established in the same geometric setting.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140573507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Complete CMC-1 surfaces in hyperbolic space with arbitrary complex structure 双曲空间中具有任意复杂结构的完整 CMC-1 曲面
IF 1.6 2区 数学
Communications in Contemporary Mathematics Pub Date : 2024-04-10 DOI: 10.1142/s0219199724500111
Antonio Alarcón, Ildefonso Castro-Infantes, Jorge Hidalgo
{"title":"Complete CMC-1 surfaces in hyperbolic space with arbitrary complex structure","authors":"Antonio Alarcón, Ildefonso Castro-Infantes, Jorge Hidalgo","doi":"10.1142/s0219199724500111","DOIUrl":"https://doi.org/10.1142/s0219199724500111","url":null,"abstract":"<p>We prove that every open Riemann surface <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>M</mi></math></span><span></span> is the complex structure of a complete surface of constant mean curvature <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mn>1</mn></math></span><span></span> (<span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">CMC-1</mtext></mstyle></math></span><span></span>) in the three-dimensional hyperbolic space <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℍ</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span><span></span>. We go further and establish a jet interpolation theorem for complete conformal <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">CMC-1</mtext></mstyle></math></span><span></span> immersions <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>M</mi><mo>→</mo><msup><mrow><mi>ℍ</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span><span></span>. As a consequence, we show the existence of complete densely immersed <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mstyle><mtext mathvariant=\"normal\">CMC-1</mtext></mstyle></math></span><span></span> surfaces in <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℍ</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span><span></span> with arbitrary complex structure. We obtain these results as application of a uniform approximation theorem with jet interpolation for holomorphic null curves in <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℂ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy=\"false\">×</mo><msup><mrow><mi>ℂ</mi></mrow><mrow><mo stretchy=\"false\">∗</mo></mrow></msup></math></span><span></span> which is also established in this paper.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140573461","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Shadowing, Hyers–Ulam stability and hyperbolicity for nonautonomous linear delay differential equations 非自治线性延迟微分方程的阴影、海尔-乌兰稳定性和双曲性
IF 1.6 2区 数学
Communications in Contemporary Mathematics Pub Date : 2024-03-27 DOI: 10.1142/s0219199724500123
Lucas Backes, Davor Dragičević, Mihály Pituk
{"title":"Shadowing, Hyers–Ulam stability and hyperbolicity for nonautonomous linear delay differential equations","authors":"Lucas Backes, Davor Dragičević, Mihály Pituk","doi":"10.1142/s0219199724500123","DOIUrl":"https://doi.org/10.1142/s0219199724500123","url":null,"abstract":"<p>It is known that hyperbolic nonautonomous linear delay differential equations in a finite dimensional space are Hyers–Ulam stable and hence shadowable. The converse result is available only in the special case of autonomous and periodic linear delay differential equations with a simple spectrum. In this paper, we prove the converse and hence the equivalence of all three notions in the title for a general class of nonautonomous linear delay differential equations with uniformly bounded coefficients. The importance of the boundedness assumption is shown by an example.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Compactified Jacobians of extended ADE curves and Lagrangian fibrations 扩展 ADE 曲线和拉格朗日纤维的紧凑雅各比
IF 1.6 2区 数学
Communications in Contemporary Mathematics Pub Date : 2024-03-09 DOI: 10.1142/s0219199724500044
Adam Czapliński, Andreas Krug, Manfred Lehn, Sönke Rollenske
{"title":"Compactified Jacobians of extended ADE curves and Lagrangian fibrations","authors":"Adam Czapliński, Andreas Krug, Manfred Lehn, Sönke Rollenske","doi":"10.1142/s0219199724500044","DOIUrl":"https://doi.org/10.1142/s0219199724500044","url":null,"abstract":"<p>We observe that general reducible curves in sufficiently positive linear systems on K3 surfaces are of a form that generalize Kodaira’s classification of singular elliptic fibers and thus call them extended ADE curves. On such a curve <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi></math></span><span></span>, we describe a compactified Jacobian and show that its components reflect the intersection graph of <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi></math></span><span></span>. This extends known results when <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi></math></span><span></span> is reduced, but new difficulties arise when <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>C</mi></math></span><span></span> is non-reduced. As an application, we get an explicit description of general singular fibers of certain Lagrangian fibrations of Beauville–Mukai type.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140168367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A global Morse index theorem and applications to Jacobi fields on CMC surfaces 全局莫尔斯指数定理及其在 CMC 表面雅可比场上的应用
IF 1.6 2区 数学
Communications in Contemporary Mathematics Pub Date : 2024-02-28 DOI: 10.1142/s0219199723500645
Wu-Hsiung Huang
{"title":"A global Morse index theorem and applications to Jacobi fields on CMC surfaces","authors":"Wu-Hsiung Huang","doi":"10.1142/s0219199723500645","DOIUrl":"https://doi.org/10.1142/s0219199723500645","url":null,"abstract":"<p>In this paper, we establish a “global” Morse index theorem. Given a hypersurface <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span><span></span> of constant mean curvature, immersed in <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℝ</mi></mrow><mrow><mi>n</mi><mo stretchy=\"false\">+</mo><mn>1</mn></mrow></msup></math></span><span></span>. Consider a continuous deformation of “generalized” Lipschitz domain <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>D</mi><mo stretchy=\"false\">(</mo><mi>t</mi><mo stretchy=\"false\">)</mo></math></span><span></span> enlarging in <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span><span></span>. The topological type of <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>D</mi><mo stretchy=\"false\">(</mo><mi>t</mi><mo stretchy=\"false\">)</mo></math></span><span></span> is permitted to change along <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>t</mi></math></span><span></span>, so that <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mi>D</mi><mo stretchy=\"false\">(</mo><mi>t</mi><mo stretchy=\"false\">)</mo></math></span><span></span> has an arbitrary shape which can “reach afar” in <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>M</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span><span></span>, i.e. cover any preassigned area. The proof of the global Morse index theorem is reduced to the continuity in <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><mi>t</mi></math></span><span></span> of the Sobolev space <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>H</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span><span></span> of variation functions on <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><mi>D</mi><mo stretchy=\"false\">(</mo><mi>t</mi><mo stretchy=\"false\">)</mo></math></span><span></span>, as well as the continuity of eigenvalues of the stability operator. We devise a “detour” strategy by introducing a notion of “set-continuity” of <span><math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><mi>D</mi><mo stretchy=\"false\">(</mo><mi>t</mi><mo stretchy=\"false\">)</mo></math></span><span></span> in <span><math altimg=\"eq-00013.gif\" display=\"inline\" overflow=\"scroll\"><mi>t</mi></math></span><span></span> to yield the required continuities of <span><math altimg=\"eq-00014.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>H</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span><span></span> and of eigenvalues. The global Morse index theorem thus follows and provides a structural theorem of the existence of Jacobi fields on domains in <span><math altimg=\"eq-00015.gif\" display=\"","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140072483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Concentration phenomena for the fractional relativistic Schrödinger–Choquard equation 分数相对论薛定谔-乔夸德方程的集中现象
IF 1.6 2区 数学
Communications in Contemporary Mathematics Pub Date : 2024-02-23 DOI: 10.1142/s021919972350061x
Vincenzo Ambrosio
{"title":"Concentration phenomena for the fractional relativistic Schrödinger–Choquard equation","authors":"Vincenzo Ambrosio","doi":"10.1142/s021919972350061x","DOIUrl":"https://doi.org/10.1142/s021919972350061x","url":null,"abstract":"<p>We consider the fractional relativistic Schrödinger–Choquard equation <disp-formula-group><span><math altimg=\"eq-00001.gif\" display=\"block\" overflow=\"scroll\"><mrow><mfenced close=\"\" open=\"{\" separators=\"\"><mrow><mtable columnlines=\"none\" equalcolumns=\"false\" equalrows=\"false\"><mtr><mtd columnalign=\"left\"><msup><mrow><mo stretchy=\"false\">(</mo><mo stretchy=\"false\">−</mo><mi mathvariant=\"normal\">Δ</mi><mo stretchy=\"false\">+</mo><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy=\"false\">)</mo></mrow><mrow><mi>s</mi></mrow></msup><mi>u</mi><mo stretchy=\"false\">+</mo><mi>V</mi><mo stretchy=\"false\">(</mo><mi>𝜀</mi><mi>x</mi><mo stretchy=\"false\">)</mo><mi>u</mi><mo>=</mo><mfenced close=\")\" open=\"(\" separators=\"\"><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>μ</mi></mrow></msup></mrow></mfrac><mo stretchy=\"false\">∗</mo><mi>F</mi><mo stretchy=\"false\">(</mo><mi>u</mi><mo stretchy=\"false\">)</mo></mrow></mfenced><mi>f</mi><mo stretchy=\"false\">(</mo><mi>u</mi><mo stretchy=\"false\">)</mo></mtd><mtd columnalign=\"left\"><mstyle><mtext>in</mtext></mstyle><mspace width=\".17em\"></mspace><mspace width=\".17em\"></mspace><msup><mrow><mi>ℝ</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd columnalign=\"left\"><mi>u</mi><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mo stretchy=\"false\">(</mo><msup><mrow><mi>ℝ</mi></mrow><mrow><mi>N</mi></mrow></msup><mo stretchy=\"false\">)</mo><mo>,</mo></mtd><mtd columnalign=\"left\"><mi>u</mi><mo>&gt;</mo><mn>0</mn><mspace width=\".17em\"></mspace><mspace width=\".17em\"></mspace><mstyle><mtext>in</mtext></mstyle><mspace width=\".17em\"></mspace><mspace width=\".17em\"></mspace><msup><mrow><mi>ℝ</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></mrow></math></span><span></span></disp-formula-group> where <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>𝜀</mi><mo>&gt;</mo><mn>0</mn></math></span><span></span> is a small parameter, <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>s</mi><mo>∈</mo><mo stretchy=\"false\">(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo stretchy=\"false\">)</mo></math></span><span></span>, <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>m</mi><mo>&gt;</mo><mn>0</mn></math></span><span></span>, <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>N</mi><mo>&gt;</mo><mn>2</mn><mi>s</mi></math></span><span></span>, <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>μ</mi><mo>∈</mo><mo stretchy=\"false\">(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mi>s</mi><mo stretchy=\"false\">)</mo></math></span><span></span>, <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mo stretchy=\"false\">(</mo><mo stretchy=\"false\">−</mo><mi mathvariant=\"normal\">Δ</mi><mo stretchy=\"false\">+</mo><msup><mrow><mi>m</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy=","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140076158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Toroidal extended affine Lie algebras and vertex algebras 环状扩展仿射李代数和顶点代数
IF 1.6 2区 数学
Communications in Contemporary Mathematics Pub Date : 2024-02-23 DOI: 10.1142/s0219199724500032
Fulin Chen, Haisheng Li, Shaobin Tan
{"title":"Toroidal extended affine Lie algebras and vertex algebras","authors":"Fulin Chen, Haisheng Li, Shaobin Tan","doi":"10.1142/s0219199724500032","DOIUrl":"https://doi.org/10.1142/s0219199724500032","url":null,"abstract":"<p>In this paper, we study nullity-<span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mn>2</mn></math></span><span></span> toroidal extended affine Lie algebras in the context of vertex algebras and their <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>ϕ</mi></math></span><span></span>-coordinated modules. Among the main results, we introduce a variant of toroidal extended affine Lie algebras, associate vertex algebras to the variant Lie algebras, and establish a canonical connection between modules for toroidal extended affine Lie algebras and <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>ϕ</mi></math></span><span></span>-coordinated modules for these vertex algebras. Furthermore, by employing some results of Billig, we obtain an explicit realization of a class of irreducible modules for the variant Lie algebras.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140072481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weight module classifications for Bershadsky–Polyakov algebras 贝尔沙德斯基-波利亚科夫代数的权重模块分类
IF 1.6 2区 数学
Communications in Contemporary Mathematics Pub Date : 2024-02-23 DOI: 10.1142/s0219199723500633
Dražen Adamović, Kazuya Kawasetsu, David Ridout
{"title":"Weight module classifications for Bershadsky–Polyakov algebras","authors":"Dražen Adamović, Kazuya Kawasetsu, David Ridout","doi":"10.1142/s0219199723500633","DOIUrl":"https://doi.org/10.1142/s0219199723500633","url":null,"abstract":"<p>The Bershadsky–Polyakov algebras are the subregular quantum Hamiltonian reductions of the affine vertex operator algebras associated with <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>𝔰</mi><mi>𝔩</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span><span></span>. In (D. Adamović, K. Kawasetsu and D. Ridout, A realisation of the Bershadsky–Polyakov algebras and their relaxed modules, <i>Lett. Math. Phys.</i><b>111</b> (2021) 38, arXiv:2007.00396 [math.QA]), we realized these algebras in terms of the regular reduction, Zamolodchikov’s <i>W</i><sub>3</sub>-algebra, and an isotropic lattice vertex operator algebra. We also proved that a natural construction of relaxed highest-weight Bershadsky–Polyakov modules has the property that the result is generically irreducible. Here, we prove that this construction, when combined with spectral flow twists, gives a complete set of irreducible weight modules whose weight spaces are finite-dimensional. This gives a simple independent proof of the main classification theorem of (Z. Fehily, K. Kawasetsu and D. Ridout, Classifying relaxed highest-weight modules for admissible-level Bershadsky–Polyakov algebras, <i>Comm. Math. Phys.</i><b>385</b> (2021) 859–904, arXiv:2007.03917 [math.RT]) for nondegenerate admissible levels and extends this classification to a category of weight modules. We also deduce the classification for the nonadmissible level <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mstyle mathvariant=\"sans-serif\"><mi>k</mi></mstyle><mo>=</mo><mo stretchy=\"false\">−</mo><mfrac><mrow><mn>7</mn></mrow><mrow><mn>3</mn></mrow></mfrac></math></span><span></span>, which is new.</p>","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140072484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Geodesics on adjoint orbits of SL(n, ℝ) SL(n, ℝ) 邻接轨道上的测地线
IF 1.6 2区 数学
Communications in Contemporary Mathematics Pub Date : 2024-02-23 DOI: 10.1142/s0219199724500019
Brian Grajales, Lino Grama, Rafaela F. Prado
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