Mathematical Research Letters最新文献

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Affine symmetries in quantum cohomology: corrections and new results 量子上同调中的仿射对称性:修正和新结果
3区 数学
Mathematical Research Letters Pub Date : 2023-01-01 DOI: 10.4310/mrl.2023.v30.n2.a3
Pierre-Emmanuel Chaput, Nicolas Perrin
{"title":"Affine symmetries in quantum cohomology: corrections and new results","authors":"Pierre-Emmanuel Chaput, Nicolas Perrin","doi":"10.4310/mrl.2023.v30.n2.a3","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n2.a3","url":null,"abstract":"In a previous paper Affine symmetries of the equivariant quantum cohomology of rational homogeneous spaces, a general formula was given for the multiplication by some special Schubert classes in the quantum cohomology of any homogeneous space. Although this formula is correct in the non equivariant setting, the stated equivariant version was wrong. We provide corrections for the equivariant formula, thus giving a correct argument for the non equivariant formula. We also give new formulas in the equivariant homology of the affine grassmannian that could lead to Pieri type formulas.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135784451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Derived categories of Quot schemes of locally free quotients via categorified Hall products 利用已分类的霍尔积导出了局部自由商的“方案”的类别
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2023-01-01 DOI: 10.4310/mrl.2023.v30.n1.a10
Yukinobu Toda
{"title":"Derived categories of Quot schemes of locally free quotients via categorified Hall products","authors":"Yukinobu Toda","doi":"10.4310/mrl.2023.v30.n1.a10","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n1.a10","url":null,"abstract":"","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Refinements of strong multiplicity one for $mathrm{GL}(2)$ $mathrm{GL}(2)的强重数一的精化$
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2022-03-20 DOI: 10.4310/mrl.2022.v29.n2.a11
PENG-JIE Wong
{"title":"Refinements of strong multiplicity one for $mathrm{GL}(2)$","authors":"PENG-JIE Wong","doi":"10.4310/mrl.2022.v29.n2.a11","DOIUrl":"https://doi.org/10.4310/mrl.2022.v29.n2.a11","url":null,"abstract":"For distinct unitary cuspidal automorphic representations π1 and π2 for GL(2) over a number field F and any α ∈ R, let Sα be the set of primes v of F for which λπ1(v) 6= eλπ2(v), where λπi(v) is the Fourier coefficient of πi at v. In this article, we show that the lower Dirichlet density of Sα is at least 1 16 . Moreover, if π1 and π2 are not twist-equivalent, we show that the lower Dirichlet densities of Sα and ∩α Sα are at least 2 13 and 1 11 , respectively. Furthermore, for non-twist-equivalent π1 and π2, if each πi corresponds to a non-CM newform of weight ki ≥ 2 and with trivial nebentypus, we obtain various upper bounds for the number of primes p ≤ x such that λπ1(p) 2 = λπ2(p) . These present refinements of the works of Murty-Pujahari, Murty-Rajan, Ramakrishnan, and Walji.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":" ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49562993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Surface Group Conjectures for groups with two generators 具有两个发生器的群的表面群猜想
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2022-02-22 DOI: 10.4310/mrl.2023.v30.n1.a5
Giles Gardam, Dawid Kielak, Alan D. Logan
{"title":"The Surface Group Conjectures for groups with two generators","authors":"Giles Gardam, Dawid Kielak, Alan D. Logan","doi":"10.4310/mrl.2023.v30.n1.a5","DOIUrl":"https://doi.org/10.4310/mrl.2023.v30.n1.a5","url":null,"abstract":"The Surface Group Conjectures are statements about recognising surface groups among one-relator groups, using either the structure of their finite-index subgroups, or all subgroups. We resolve these conjectures in the two generator case. More generally, we prove that every two-generator one-relator group with every infinite-index subgroup free is itself either free or a surface group.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46449068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 2
Internal stabilization for KdV-BBM equation on a periodic domain 周期域上KdV-BBM方程的内镇定
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2022-01-01 DOI: 10.4310/mrl.2022.v29.n6.a4
Melek Jellouli, M. Khenissi
{"title":"Internal stabilization for KdV-BBM equation on a periodic domain","authors":"Melek Jellouli, M. Khenissi","doi":"10.4310/mrl.2022.v29.n6.a4","DOIUrl":"https://doi.org/10.4310/mrl.2022.v29.n6.a4","url":null,"abstract":"","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 local information of difference equations 差分方程的局部信息
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2022-01-01 DOI: 10.4310/mrl.2022.v29.n1.a5
Moisés Herradón Cueto
{"title":"The local information of difference equations","authors":"Moisés Herradón Cueto","doi":"10.4310/mrl.2022.v29.n1.a5","DOIUrl":"https://doi.org/10.4310/mrl.2022.v29.n1.a5","url":null,"abstract":"","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Diagrams of $star$-trisections $星$-三切分图
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2022-01-01 DOI: 10.4310/mrl.2022.v29.n6.a1
Rom'an Aranda, Jesse Moeller
{"title":"Diagrams of $star$-trisections","authors":"Rom'an Aranda, Jesse Moeller","doi":"10.4310/mrl.2022.v29.n6.a1","DOIUrl":"https://doi.org/10.4310/mrl.2022.v29.n6.a1","url":null,"abstract":"","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Convex hull property for ancient harmonic map heat flows 古调和图热流的凸壳性
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2022-01-01 DOI: 10.4310/mrl.2022.v29.n5.a12
C. Sung
{"title":"Convex hull property for ancient harmonic map heat flows","authors":"C. Sung","doi":"10.4310/mrl.2022.v29.n5.a12","DOIUrl":"https://doi.org/10.4310/mrl.2022.v29.n5.a12","url":null,"abstract":"","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
New $k$-th Yau algebras of isolated hypersurface singularities and weak Torelli-type theorem 孤立超曲面奇点的新$k$-th Yau代数及弱torelli型定理
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2022-01-01 DOI: 10.4310/mrl.2022.v29.n2.a7
Naveed Hussain, S. Yau, Huaiqing Zuo
{"title":"New $k$-th Yau algebras of isolated hypersurface singularities and weak Torelli-type theorem","authors":"Naveed Hussain, S. Yau, Huaiqing Zuo","doi":"10.4310/mrl.2022.v29.n2.a7","DOIUrl":"https://doi.org/10.4310/mrl.2022.v29.n2.a7","url":null,"abstract":"Let V be a hypersurface with an isolated singularity at the origin defined by the holomorphic function f : ( C n , 0) → ( C , 0). The Yau algebra L ( V ) is defined to be the Lie algebra of derivations of the moduli algebra A ( V ) := O n / ( f, ∂f∂x 1 , · · · , ∂f∂x n ), i.e., L ( V ) = Der( A ( V ) , A ( V )). It is known that L ( V ) is a finite dimensional Lie algebra and its dimension λ ( V ) is called Yau number. In this paper, we introduce a new series of Lie algebras, i.e., k -th Yau algebras L k ( V ), k ≥ 0, which are a generalization of Yau algebra. L k ( V ) is defined to be the Lie algebra of derivations of the k th moduli algebra A k ( V ) := O n / ( f, m k J ( f )) , k ≥ 0, i.e., L k ( V ) = Der( A k ( V ) , A k ( V )), where m is the maximal ideal of O n . The k -th Yau number is the dimension of L k ( V ) which we denote as λ k ( V ). In particular, L 0 ( V ) is exactly the Yau algebra, i.e., L 0 ( V ) = L ( V ) , λ 0 ( V ) = λ ( V ). These numbers λ k ( V ) are new numerical analytic invariants of singularities. In this paper we obtain the weak Torelli-type theorems of simple elliptic singularities using Lie algebras L 1 ( V ) and L 2 ( V ). We shall also characterize the simple singularities completely using L 1 ( V ).","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 6
Symplectic duality for $T^ast Gr(k, n)$ T^ast Gr(k, n)的辛对偶性
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2022-01-01 DOI: 10.4310/mrl.2022.v29.n3.a3
Hunter Dinkins
{"title":"Symplectic duality for $T^ast Gr(k, n)$","authors":"Hunter Dinkins","doi":"10.4310/mrl.2022.v29.n3.a3","DOIUrl":"https://doi.org/10.4310/mrl.2022.v29.n3.a3","url":null,"abstract":"","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70517043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
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