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Representations of Reductive Groups最新文献

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Geometric approach to the fermionic Fock space, via flag varieties and representations of algebraic (super)groups 费米子Fock空间的几何方法，通过标志变异和代数(超)群的表示
Representations of Reductive Groups Pub Date : 2019-02-19 DOI: 10.1090/pspum/101/07
Caroline Gruson, V. Serganova
{"title":"Geometric approach to the fermionic Fock\u0000 space, via flag varieties and representations of\u0000 algebraic (super)groups","authors":"Caroline Gruson, V. Serganova","doi":"10.1090/pspum/101/07","DOIUrl":"https://doi.org/10.1090/pspum/101/07","url":null,"abstract":"","PeriodicalId":237232,"journal":{"name":"Representations of Reductive Groups","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125545677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The modular pro-𝑝 Iwahori-Hecke Ext-algebra 模pro-𝑝Iwahori-Hecke ext -代数
Representations of Reductive Groups Pub Date : 2019-02-19 DOI: 10.1090/pspum/101/11
Rachel Ollivier, P. Schneider
{"title":"The modular pro-𝑝 Iwahori-Hecke\u0000 Ext-algebra","authors":"Rachel Ollivier, P. Schneider","doi":"10.1090/pspum/101/11","DOIUrl":"https://doi.org/10.1090/pspum/101/11","url":null,"abstract":"Let F be a locally compact nonarchimedean field of positive residue characteristic p and k a field of characteristic p. Let G be the group of F-rational points of a connected reductive group over F which we suppose F-split. Given a pro-p Iwahori subgroup I of G, we consider the space X of k-valued functions with compact support on G/I. It is naturally an object in the category Mod(G) of all smooth k-representations of G. We study the graded Ext-algebra E∗ = ExtMod(G)(X,X). Its degree zero piece E 0 is the usual pro-p Iwahori Hecke algebra H. We describe the product in E∗ and provide an involutive anti-automorphism of E∗. When I is a Poincaré group of dimension d, the Extalgebra E∗ is supported in degrees i ∈ {0 . . . d} and we establish a duality theorem between E and Ed−i. Under the same hypothesis (and assuming that G is almost simple and simply connected), we compute E as an H-module on the left and on the right. We prove that it is a direct sum of the trivial character, and of supersingular modules.","PeriodicalId":237232,"journal":{"name":"Representations of Reductive Groups","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125537865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 14
Representations of a 𝑝-adic group in characteristic 𝑝 特征𝑝中𝑝-adic组的表示
Representations of Reductive Groups Pub Date : 2019-02-19 DOI: 10.1090/pspum/101/08
G. Henniart, M. Vigneras
{"title":"Representations of a 𝑝-adic group in\u0000 characteristic 𝑝","authors":"G. Henniart, M. Vigneras","doi":"10.1090/pspum/101/08","DOIUrl":"https://doi.org/10.1090/pspum/101/08","url":null,"abstract":"","PeriodicalId":237232,"journal":{"name":"Representations of Reductive Groups","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114336900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Periods and theta correspondence 周期和对应关系
Representations of Reductive Groups Pub Date : 2019-02-19 DOI: 10.1090/pspum/101/05
W. Gan
{"title":"Periods and theta correspondence","authors":"W. Gan","doi":"10.1090/pspum/101/05","DOIUrl":"https://doi.org/10.1090/pspum/101/05","url":null,"abstract":"","PeriodicalId":237232,"journal":{"name":"Representations of Reductive Groups","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133564942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
On vector-valued twisted conjugation invariant functions on a group; with an appendix by Stephen Donkin 群上的向量值扭共轭不变量函数附斯蒂芬·唐金的附录
Representations of Reductive Groups Pub Date : 2019-02-19 DOI: 10.1090/pspum/101/14
L. Xiao, Xinwen Zhu
{"title":"On vector-valued twisted conjugation\u0000 invariant functions on a group; with an appendix by\u0000 Stephen Donkin","authors":"L. Xiao, Xinwen Zhu","doi":"10.1090/pspum/101/14","DOIUrl":"https://doi.org/10.1090/pspum/101/14","url":null,"abstract":"","PeriodicalId":237232,"journal":{"name":"Representations of Reductive Groups","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131768304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalized and degenerate Whittaker quotients and Fourier coefficients 广义简并惠特克商和傅里叶系数
Representations of Reductive Groups Pub Date : 2018-07-30 DOI: 10.1090/pspum/101/06
D. Gourevitch, S. Sahi
{"title":"Generalized and degenerate Whittaker\u0000 quotients and Fourier coefficients","authors":"D. Gourevitch, S. Sahi","doi":"10.1090/pspum/101/06","DOIUrl":"https://doi.org/10.1090/pspum/101/06","url":null,"abstract":"The study of Whittaker models for representations of reductive groups over local and global fields has become a central tool in representation theory and the theory of automorphic forms. However, only generic representations have Whittaker models. In order to encompass other representations, one attaches a degenerate (or a generalized) Whittaker model $W_{mathcal{O}}$, or a Fourier coefficient in the global case, to any nilpotent orbit $mathcal{O}$. In this note we survey some classical and some recent work in this direction - for Archimedean, p-adic and global fields. The main results concern the existence of models. For a representation $pi$, call the set of maximal orbits $mathcal{O}$ with $W_{mathcal{O}}$ that includes $pi$ the Whittaker support of $pi$. The two main questions discussed in this note are: (1) What kind of orbits can appear in the Whittaker support of a representation? (2) How does the Whittaker support of a given representation $pi$ relate to other invariants of $pi$, such as its wave-front set?","PeriodicalId":237232,"journal":{"name":"Representations of Reductive Groups","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123051999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Affine Hecke algebras and the conjectures of Hiraga, Ichino and Ikeda on the Plancherel density 仿射Hecke代数及Hiraga、Ichino和Ikeda关于Plancherel密度的猜想
Representations of Reductive Groups Pub Date : 2018-07-26 DOI: 10.1090/pspum/101/12
E. Opdam
{"title":"Affine Hecke algebras and the conjectures of\u0000 Hiraga, Ichino and Ikeda on the Plancherel\u0000 density","authors":"E. Opdam","doi":"10.1090/pspum/101/12","DOIUrl":"https://doi.org/10.1090/pspum/101/12","url":null,"abstract":"Hiraga, Ichino and Ikeda have conjectured an explicit expression for the Plancherel density of the group of points of a reductive group defined over a local field $F$, in terms of local Langlands parameters. In these lectures we shall present a proof of these conjectures for Lusztig's class of representations of unipotent reduction if $F$ is $p$-adic and $G$ is of adjoint type and splits over an unramified extension of $F$. This is based on the author's paper [Spectral transfer morphisms for unipotent affine Hecke algebras, Selecta Math. (N.S.) 22 (2016), no. 4, 2143--2207]. \u0000More generally for $G$ connected reductive (still assumed to be split over an unramified extension of $F$), we shall show that the requirement of compatibility with the conjectures of Hiraga, Ichino and Ikeda essentially determines the Langlands parameterisation for tempered representations of unipotent reduction. We shall show that there exist parameterisations for which the conjectures of Hiraga, Ichino and Ikeda hold up to rational constant factors. The main technical tool is that of spectral transfer maps between normalised affine Hecke algebras used in op. cit.","PeriodicalId":237232,"journal":{"name":"Representations of Reductive Groups","volume":"200 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116225570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Schwartz space of parabolic basic affine space and asymptotic Hecke algebras 抛物型基本仿射空间的Schwartz空间与渐近Hecke代数
Representations of Reductive Groups Pub Date : 2018-04-01 DOI: 10.1090/pspum/101/02
A. Braverman, D. Kazhdan
{"title":"Schwartz space of parabolic basic affine\u0000 space and asymptotic Hecke algebras","authors":"A. Braverman, D. Kazhdan","doi":"10.1090/pspum/101/02","DOIUrl":"https://doi.org/10.1090/pspum/101/02","url":null,"abstract":"Let $F$ be a local non-archimedian field and $G$ be the group of $F$-points of a split connected reductive group over $F$. In a previous aricle we defined an algebra $mathcal J(G)$ of functions on $G$ which contains the Hecke algebra $mathcal H(G)$ and is contained in the Harish-Chandra Schwartz algebra $mathcal C(G)$. We consider $mathcal J(G)$ as an algebraic analog the algebra $mathcal C(G)$. Given a parabolic subgroup $P$ of $G$ with a Levi subgroup $M$ and the unipotent radical $U_P$ we write $X_P:=G/U_P$. In this paper we study two versions of the Schwartz space of $X_P$. The first is $mathcal S(X_P):=matcal J(mathcal S _c(X_P))$ and the 2nd is the space spanned by functions of the form $Phi_{Q,P}(phi)$ where $Q$ is another parabolic with the same Levi subgroup, $phiin mathcal S_c(X_Q)$ and $Phi_{Q,P}$ is a normalized intertwining operator from $L^2(X_Q)$ to $L^2(X_P)$. We formulate a series of conjectures about these spaces, for example, we conjecture that $mathcal S'(X_P)subset mathcal S(X_P)$ and that this embedding is an isomorphism on $M$-cuspidal part. We give a proof of some of our conjectures.","PeriodicalId":237232,"journal":{"name":"Representations of Reductive Groups","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127007598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Character values and Hochschild homology 字符值与Hochschild同调
Representations of Reductive Groups Pub Date : 2018-03-26 DOI: 10.1090/pspum/101/01
R. Bezrukavnikov, D. Kazhdan
{"title":"Character values and Hochschild\u0000 homology","authors":"R. Bezrukavnikov, D. Kazhdan","doi":"10.1090/pspum/101/01","DOIUrl":"https://doi.org/10.1090/pspum/101/01","url":null,"abstract":"We present a conjecture (and a proof for G=SL(2)) generalizing a result of J. Arthur which expresses a character value of a cuspidal representation of a $p$-adic group as a weighted orbital integral of its matrix coefficient. It also generalizes a conjecture by the second author proved by Schneider-Stuhler and (independently) the first author. The latter statement expresses an elliptic character value as an orbital integral of a pseudo-matrix coefficient defined via the Chern character map taking value in zeroth Hochschild homology of the Hecke algebra. The present conjecture generalizes the construction of pseudo-matrix coefficient using compactly supported Hochschild homology, as well as a modification of the category of smooth representations, the so called compactified category of smooth $G$-modules. This newly defined \"compactified pseudo-matrix coefficient\" lies in a certain space on which the weighted orbital integral is a conjugation invariant linear functional, our conjecture states that evaluating a weighted orbital integral on the compactified pseudo-matrix coefficient one recovers the corresponding character value of the representation. We also discuss general properties of that space, building on works of Waldspurger and Beuzart-Plessis.","PeriodicalId":237232,"journal":{"name":"Representations of Reductive Groups","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131120603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the support of matrix coefficients of supercuspidal representations of the general linear group over a local non-archimedean field 局部非阿基米德域上一般线性群的超尖表示的矩阵系数支持
Representations of Reductive Groups Pub Date : 2018-02-20 DOI: 10.1090/pspum/101/09
E. Lapid
{"title":"On the support of matrix coefficients of\u0000 supercuspidal representations of the general linear\u0000 group over a local non-archimedean field","authors":"E. Lapid","doi":"10.1090/pspum/101/09","DOIUrl":"https://doi.org/10.1090/pspum/101/09","url":null,"abstract":"We derive an upper bound on the support of matrix coefficients of suprecuspidal representations of the general linear group over a non-archimedean local field. The results are in par with those which can be obtained from the Bushnell--Kutzko classification of supercuspidal representations, but they are proved independently.","PeriodicalId":237232,"journal":{"name":"Representations of Reductive Groups","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128998545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
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