Japanese Journal of Mathematics最新文献_第2页

Grothendieck spaces: the landscape and perspectives 格罗滕迪克空间:景观和视角

IF 1.5 3区数学

Japanese Journal of Mathematics Pub Date : 2021-02-07 DOI: 10.1007/s11537-021-2116-3

Manuel Gonz'alez, Tomasz Kania

引用次数: 10

Classical and variational Poisson cohomology 经典和变分泊松上同

IF 1.5 3区数学

Japanese Journal of Mathematics Pub Date : 2021-01-26 DOI: 10.1007/s11537-021-2109-2

B. Bakalov, Alberto De Sole, Reimundo Heluani, V. Kac, V. Vignoli

引用次数: 6

Information geometry 几何信息

IF 1.5 3区数学

Japanese Journal of Mathematics Pub Date : 2021-01-02 DOI: 10.1007/s11537-020-1920-5

Shun-ichi Amari

引用次数: 0

Infinite-dimensional (dg) Lie algebras and factorization algebras in algebraic geometry 代数几何中的无限维李代数与分解代数

IF 1.5 3区数学

Japanese Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.1007/s11537-020-1921-4

M. Kapranov

引用次数: 1

Topological-antitopological fusion and the quantum cohomology of Grassmannians 拓扑反拓扑融合与Grassmanns的量子上同调

IF 1.5 3区数学

Japanese Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.1007/s11537-020-2036-7

M. Guest

引用次数: 4

K-theory and G-theory of derived algebraic stacks 派生代数堆栈的k理论和g理论

IF 1.5 3区数学

Japanese Journal of Mathematics Pub Date : 2020-12-13 DOI: 10.1007/s11537-021-2110-9

Adeel A. Khan

引用次数: 13

The lattice of varieties of monoids 一元群的各种格

IF 1.5 3区数学

Japanese Journal of Mathematics Pub Date : 2020-11-07 DOI: 10.1007/s11537-022-2073-5

S. V. Gusev, Edmond W. H. Lee, B. M. Vernikov

引用次数: 7

Rank and duality in representation theory 表征理论中的秩与对偶

IF 1.5 3区数学

Japanese Journal of Mathematics Pub Date : 2020-05-19 DOI: 10.1007/s11537-020-1728-3

Shamgar Gurevich, Roger Howe

{"title":"Rank and duality in representation theory","authors":"Shamgar Gurevich, Roger Howe","doi":"10.1007/s11537-020-1728-3","DOIUrl":"https://doi.org/10.1007/s11537-020-1728-3","url":null,"abstract":"There is both theoretical and numerical evidence that the set of irreducible representations of a reductive group over local or finite fields is naturally partitioned into families according to analytic properties of representations. Examples of such properties are the rate of decay at infinity of “matrix coefficients” in the local field setting, and the order of magnitude of “character ratios” in the finite field situation.In these notes we describe known results, new results, and conjectures in the theory of “size” of representations of classical groups over finite fields (when correctly stated, most of them hold also in the local field setting), whose ultimate goal is to classify the above mentioned families of representations and accordingly to estimate the relevant analytic properties of each family.Specifically, we treat two main issues: the first is the introduction of a rigorous definition of a notion of size for representations of classical groups, and the second issue is a method to construct and obtain information on each family of representation of a given size.In particular, we propose several compatible notions of size that we call U-rank, tensor rank and asymptotic rank, and we develop a method called eta correspondence to construct the families of representation of each given rank.Rank suggests a new way to organize the representations of classical groups over finite and local fields—a way in which the building blocks are the “smallest” representations. This is in contrast to Harish-Chandra’s philosophy of cusp forms that is the main organizational principle since the 60s, and in it the building blocks are the cuspidal representations which are, in some sense, the “largest”. The philosophy of cusp forms is well adapted to establishing the Plancherel formula for reductive groups over local fields, and led to Lusztig’s classification of the irreducible representations of such groups over finite fields. However, the understanding of certain analytic properties, such as those mentioned above, seems to require a different approach.","PeriodicalId":54908,"journal":{"name":"Japanese Journal of Mathematics","volume":"137 ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2020-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505936","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: 11

Transgressions of the Euler class and Eisenstein cohomology of GL N (Z) GL N (Z)的欧拉类越界与爱森斯坦上同

IF 1.5 3区数学

Japanese Journal of Mathematics Pub Date : 2020-03-04 DOI: 10.1007/s11537-019-1822-6

Nicolas Bergeron, Pierre Charollois, Luis E. Garcia

{"title":"Transgressions of the Euler class and Eisenstein cohomology of GL N (Z)","authors":"Nicolas Bergeron, Pierre Charollois, Luis E. Garcia","doi":"10.1007/s11537-019-1822-6","DOIUrl":"https://doi.org/10.1007/s11537-019-1822-6","url":null,"abstract":"These notes were written to be distributed to the audience of the first author’s Takagi Lectures delivered June 23, 2018. These are based on a work-in-progress that is part of a collaborative project that also involves Akshay Venkatesh.In this work-in-progress we give a new construction of some Eisenstein classes for GLN (Z) that were first considered by Nori [41] and Sczech [44]. The starting point of this construction is a theorem of Sullivan on the vanishing of the Euler class of SLN (Z) vector bundles and the explicit transgression of this Euler class by Bismut and Cheeger. Their proof indeed produces a universal form that can be thought of as a kernel for a regularized theta lift for the reductive dual pair (GLN, GL1). This suggests looking to reductive dual pairs (GLN, GLk) with k ≥ 1 for possible generalizations of the Eisenstein cocycle. This leads to fascinating lifts that relate the geometry/topology world of real arithmetic locally symmetric spaces to the arithmetic world of modular forms.In these notes we do not deal with the most general cases and put a lot of emphasis on various examples that are often classical.","PeriodicalId":54908,"journal":{"name":"Japanese Journal of Mathematics","volume":"129 ","pages":""},"PeriodicalIF":1.5,"publicationDate":"2020-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138505941","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: 12

Computation of cohomology of vertex algebras 顶点代数上同调的计算

IF 1.5 3区数学

Japanese Journal of Mathematics Pub Date : 2020-02-10 DOI: 10.1007/s11537-020-2034-9

B. Bakalov, Alberto De Sole, V. Kac

引用次数: 10