Algebras and Representation Theory最新文献_第5页

Almost Commuting Scheme of Symplectic Matrices and Quantum Hamiltonian Reduction 交映矩阵的几乎共通方案与量子哈密顿还原

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-07-17 DOI: 10.1007/s10468-024-10275-9

Pallav Goyal

{"title":"Almost Commuting Scheme of Symplectic Matrices and Quantum Hamiltonian Reduction","authors":"Pallav Goyal","doi":"10.1007/s10468-024-10275-9","DOIUrl":"10.1007/s10468-024-10275-9","url":null,"abstract":"<div>Losev introduced the scheme X of almost commuting elements (i.e., elements commuting upto a rank one element) of (mathfrak {g}=mathfrak {sp}(V)) for a symplectic vector space V and discussed its algebro-geometric properties. We construct a Lagrangian subscheme (X^{nil}) of X and show that it is a complete intersection of dimension (text {dim}(mathfrak {g})+frac{1}{2}text {dim}(V)) and compute its irreducible onents. We also study the quantum Hamiltonian reduction of the algebra (mathcal {D}(mathfrak {g})) of differential operators on the Lie algebra (mathfrak {g}) tensored with the Weyl algebra with respect to the action of the symplectic group, and show that it is isomorphic to the spherical subalgebra of a certain rational Cherednik algebra of Type C. We contruct a category (mathcal {C}_c) of (mathcal {D})-modules whose characteristic variety is contained in (X^{nil}) and construct an exact functor from this category to the category (mathcal {O}) of the above rational Cherednik algebra. Simple objects of the category (mathcal {C}_c) are mirabolic analogs of Lusztig’s character sheaves.</div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 4","pages":"1645 - 1669"},"PeriodicalIF":0.5,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-024-10275-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141718902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Localization of Triangulated Categories with Respect to Extension-Closed Subcategories 关于外延封闭子范畴的三角范畴本地化

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-05-31 DOI: 10.1007/s10468-024-10272-y

Yasuaki Ogawa

{"title":"Localization of Triangulated Categories with Respect to Extension-Closed Subcategories","authors":"Yasuaki Ogawa","doi":"10.1007/s10468-024-10272-y","DOIUrl":"10.1007/s10468-024-10272-y","url":null,"abstract":"<div>The aim of this paper is to develop a framework for localization theory of triangulated categories (mathcal {C}), that is, from a given extension-closed subcategory (mathcal {N}) of (mathcal {C}), we construct a natural extriangulated structure on (mathcal {C}) together with an exact functor (Q:mathcal {C}rightarrow widetilde{mathcal {C}}_mathcal {N}) satisfying a suitable universality, which unifies several phenomena. Precisely, a given subcategory (mathcal {N}) is thick if and only if the localization (widetilde{mathcal {C}}_mathcal {N}) corresponds to a triangulated category. In this case, Q is nothing other than the usual Verdier quotient. Furthermore, it is revealed that (widetilde{mathcal {C}}_mathcal {N}) is an exact category if and only if (mathcal {N}) satisfies a generating condition (textsf{Cone}(mathcal {N},mathcal {N})=mathcal {C}). Such an (abelian) exact localization (widetilde{mathcal {C}}_mathcal {N}) provides a good understanding of some cohomological functors (mathcal {C}rightarrow textsf{Ab}), e.g., the heart of t-structures on (mathcal {C}) and the abelian quotient of (mathcal {C}) by a cluster-tilting subcategory (mathcal {N}).</div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 3","pages":"1603 - 1640"},"PeriodicalIF":0.5,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141197677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Birational Maps to Grassmannians, Representations and Poset Polytopes 通向格拉斯曼、表征和 Poset 多面体的双向映射

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-05-30 DOI: 10.1007/s10468-024-10273-x

Evgeny Feigin

引用次数: 0

On a Generalized Auslander-Reiten Conjecture 关于广义奥斯兰德-雷滕猜想

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-05-17 DOI: 10.1007/s10468-024-10271-z

Souvik Dey, Shinya Kumashiro, Parangama Sarkar

{"title":"On a Generalized Auslander-Reiten Conjecture","authors":"Souvik Dey, Shinya Kumashiro, Parangama Sarkar","doi":"10.1007/s10468-024-10271-z","DOIUrl":"10.1007/s10468-024-10271-z","url":null,"abstract":"<div>It is well-known that the generalized Auslander-Reiten condition (GARC) and the symmetric Auslander condition (SAC) are equivalent, and (GARC) implies that the Auslander-Reiten condition (ARC). In this paper we explore (SAC) along with the several canonical change of rings (R rightarrow S). First, we prove the equivalence of (SAC) for R and R/xR, where x is a non-zerodivisor on R, and the equivalence of (SAC) and (SACC) for rings with positive depth, where (SACC) is the symmetric Auslander condition for modules with constant rank. The latter assertion affirmatively answers a question posed by Celikbas and Takahashi. Secondly, for a ring homomorphism (R rightarrow S), we prove that if S satisfies (SAC) (resp. (ARC)), then R also satisfies (SAC) (resp. (ARC)) if the flat dimension of S over R is finite. We also prove that (SAC) holds for R implies that (SAC) holds for S when R is Gorenstein and (S=R/Q^ell ), where Q is generated by a regular sequence of R and the length of the sequence is at least (ell ). This is a consequence of more general results about Ulrich ideals proved in this paper. Applying these results to determinantal rings and numerical semigroup rings, we provide new classes of rings satisfying (SAC). A relation between (SAC) and an invariant related to the finitistic extension degree is also explored.</div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 3","pages":"1581 - 1602"},"PeriodicalIF":0.5,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141061936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Twisted Representations of the Extended Heisenberg-Virasoro Vertex Operator Algebra 扩展海森堡-维拉索罗顶点算子代数的扭曲表示

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-04-30 DOI: 10.1007/s10468-024-10270-0

Hongyan Guo, Huaimin Li

{"title":"Twisted Representations of the Extended Heisenberg-Virasoro Vertex Operator Algebra","authors":"Hongyan Guo, Huaimin Li","doi":"10.1007/s10468-024-10270-0","DOIUrl":"10.1007/s10468-024-10270-0","url":null,"abstract":"<div>In this paper, we study simple weak and ordinary twisted modules of the extended Heisenberg-Virasoro vertex operator algebra (V_{tilde{mathcal {L}}_{F}}(ell _{123},0)). We first determine the full automorphism groups of (V_{tilde{mathcal {L}}_{F}}(ell _{123},0)) for all (ell _{1}, ell _{2},ell _{3},Fin {mathbb C}). They are isomorphic to certain subgroups of the general linear group (text {GL}_{2}({mathbb C})). Then for a family of finite order automorphisms (sigma _{r_{1},r_{2}}) of (V_{tilde{mathcal {L}}_{F}}(ell _{123},0)), we show that weak (sigma _{r_{1},r_{2}})-twisted (V_{tilde{mathcal {L}}_{F}}(ell _{123},0))-modules are in one-to-one correspondence with restricted modules of certain Lie algebras of level (ell _{123}), where (r_{1}, r_2in {mathbb N}). By this identification and vertex algebra theory, we give complete lists of simple ordinary (sigma _{r_{1},r_{2}})-twisted modules over (V_{tilde{mathcal {L}}_{F}}(ell _{123},0)). The results depend on whether F or (ell _{2}) is zero or not. Furthermore, simple weak (sigma _{r_{1},r_{2}})-twisted (V_{tilde{mathcal {L}}_{F}}(ell _{123},0))-modules are also investigated. For this, we introduce and study restricted modules (including Whittaker modules) of a new Lie algebra (mathcal {L}_{r_{1},r_{2}}) which is related to the mirror Heisenberg-Virasoro algebra.</div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 3","pages":"1563 - 1580"},"PeriodicalIF":0.5,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140833522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

The Mukai Conjecture for Fano Quiver Moduli 法诺震颤模的向猜想

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-04-26 DOI: 10.1007/s10468-024-10268-8

Markus Reineke

引用次数: 0

Galleries for Root Subsystems 根子系统图库

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-04-24 DOI: 10.1007/s10468-024-10269-7

Vladimir Shchigolev

引用次数: 0

Decompositions of Infinite-Dimensional (A_{infty , infty }) Quiver Representations 无穷维 $$A_{infty , infty }$$ 箙代表的分解

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-04-19 DOI: 10.1007/s10468-024-10267-9

Nathaniel Gallup, Stephen Sawin

{"title":"Decompositions of Infinite-Dimensional (A_{infty , infty }) Quiver Representations","authors":"Nathaniel Gallup, Stephen Sawin","doi":"10.1007/s10468-024-10267-9","DOIUrl":"10.1007/s10468-024-10267-9","url":null,"abstract":"<div>Gabriel’s Theorem states that the quivers which have finitely many isomorphism classes of indecomposable representations are exactly those with underlying graph one of the ADE Dynkin diagrams and that the indecomposables are in bijection with the positive roots of this graph. When the underlying graph is (varvec{A_n}), these indecomposable representations are thin (either 0 or 1 dimensional at every vertex) and in bijection with the connected subquivers. Using linear algebraic methods we show that every (possibly infinite-dimensional) representation of a quiver with underlying graph (varvec{A_{infty , infty }}) is infinite Krull-Schmidt, i.e. a direct sum of indecomposables, as long as the arrows in the quiver eventually point outward. We furthermore prove that these indecomposable are again thin and in bijection with both the connected subquivers and the limits of the positive roots of (varvec{A_{infty , infty }}) with respect to a certain uniform topology on the root space. Finally we give an example of an (varvec{A_{infty , infty }}) quiver which is not infinite Krull-Schmidt and hence necessarily is not eventually-outward.</div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1513 - 1535"},"PeriodicalIF":0.5,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10468-024-10267-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140626695","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Recasting the Hazrat Conjecture: Relating Shift Equivalence to Graded Morita Equivalence 重塑哈兹拉特猜想：移位等价性与梯度莫里塔等价性的关系

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-04-09 DOI: 10.1007/s10468-024-10266-w

Gene Abrams, Efren Ruiz, Mark Tomforde

引用次数: 0

Gelfand-Tsetlin Modules: Canonicity and Calculations 格尔凡-采特林模块：可达性和计算

IF 0.5 4区数学

Algebras and Representation Theory Pub Date : 2024-03-27 DOI: 10.1007/s10468-024-10264-y

Turner Silverthorne, Ben Webster

{"title":"Gelfand-Tsetlin Modules: Canonicity and Calculations","authors":"Turner Silverthorne, Ben Webster","doi":"10.1007/s10468-024-10264-y","DOIUrl":"10.1007/s10468-024-10264-y","url":null,"abstract":"<div>In this paper, we give a more down-to-earth introduction to the connection between Gelfand-Tsetlin modules over (mathfrak {gl}_n) and diagrammatic KLRW algebras and develop some of its consequences. In addition to a new proof of this description of the category Gelfand-Tsetlin modules appearing in earlier work, we show three new results of independent interest: (1) we show that every simple Gelfand-Tsetlin module is a canonical module in the sense of Early, Mazorchuk and Vishnyakova, and characterize when two maximal ideals have isomorphic canonical modules, (2) we show that the dimensions of Gelfand-Tsetlin weight spaces in simple modules can be computed using an appropriate modification of Leclerc’s algorithm for computing dual canonical bases, and (3) we construct a basis of the Verma modules of (mathfrak {sl}_n) which consists of generalized eigenvectors for the Gelfand-Tsetlin subalgebra. Furthermore, we present computations of multiplicities and Gelfand-Kirillov dimensions for all integral Gelfand-Tsetlin modules in ranks 3 and 4; unfortunately, for ranks (>4), our computers are not adequate to perform these computations.</div>","PeriodicalId":50825,"journal":{"name":"Algebras and Representation Theory","volume":"27 2","pages":"1405 - 1455"},"PeriodicalIF":0.5,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140312674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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