# Representation Theory of the American Mathematical Society (Represent Theor)

Publisher: American Mathematical Society, American Mathematical Society

## Journal description

This electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content.

## Impact Factor Rankings

2015 Impact Factor Available summer 2016 0.732 0.475

5-year impact 0.00 7.30 0.22 0.00 0.00 Representation Theory website Representation theory 1088-4165 34602921 Document, Internet resource Internet Resource, Computer File, Journal / Magazine / Newspaper

## Publisher details

• Pre-print
• Author can archive a pre-print version
• Post-print
• Author can archive a post-print version
• Conditions
• On author's personal website, institutional repository, open access repositories and arXiv
• Must include set publisher statement - (First published in [Publication] in [volume and number, or year], published by the American Mathematical Society)
• Publisher's version/PDF cannot be used
• Non-commercial
• Eligible UK authors may deposit in OpenDepot
• Classification
green

## Publications in this journal

• ##### Article: L’involution de Zelevinski modulo $\ell Representation Theory of the American Mathematical Society 10/2015; 19(10):236-262. DOI:10.1090/ert/466 • ##### Article: Classification of discrete series by minimal$K$-type Representation Theory of the American Mathematical Society 10/2015; 19(7):167-185. DOI:10.1090/ert/467 • ##### Article: Corrections to: “On the$\mathfrak n$-cohomology of limits of discrete series representations” Representation Theory of the American Mathematical Society 01/2015; 19(1):1-2. DOI:10.1090/S1088-4165-2015-00460-1 • Source ##### Article: A Katsylo theorem for sheets of spherical conjugacy classes [Hide abstract] ABSTRACT: We show that, for a sheet or a Lusztig stratum S containing spherical conjugacy classes in a connected reductive algebraic group G over an algebraically closed field in good characteristic, the orbit space S/G is isomorphic to the quotient of an affine subvariety of G modulo the action of a finite abelian 2-group. The affine subvariety is a closed subset of a Bruhat double coset and the abelian group is a finite subgroup of a maximal torus of G. We show that sheets of spherical conjugacy classes in a simple group are always smooth and we list which strata containing spherical classes are smooth. Representation Theory of the American Mathematical Society 01/2015; 19(11). DOI:10.1090/ert/470 • Source ##### Article: Some power series involving involutions in Coxeter groups [Hide abstract] ABSTRACT: Let W be a Coxeter group. We show that a certain power series involving a sum over all involutions in W can be expressed in terms of the Poincare series of W, at least in the case where W is an affine Weyl group. (The case where W is finite is already known,) Representation Theory of the American Mathematical Society 11/2014; 19(12). DOI:10.1090/ert/472 • Source ##### Article: Borel subgroups adapted to nilpotent elements of standard Levi type [Hide abstract] ABSTRACT: Let a reductive algebraic group over an algebraically closed field of good characteristic be given. Attached to a nilpotent element of its Lie algebra, we consider a family of algebraic varieties, which incorporates classical objects such as Springer fiber, Spaltenstein varieties, and Hessenberg varieties. When the nilpotent element is of standard Levi type, we show that the varieties of this family admit affine pavings that can be obtained by intersecting with the Schubert cells corresponding to a suitable Borel subgroup. Representation Theory of the American Mathematical Society 10/2014; 18(11):341-360. DOI:10.1090/S1088-4165-2014-00458-8 • Source ##### Article: The bar involution for quantum symmetric pairs [Hide abstract] ABSTRACT: We construct a bar involution for quantum symmetric pair coideal subalgebras$B_{\mathbf{c},\mathbf{s}}$corresponding to involutive automorphisms of the second kind of symmetrizable Kac-Moody algebras. To this end we give unified presentations of these algebras in terms of generators and relations extending previous results by G. Letzter and the second named author. We specify precisely the set of parameters$\mathbf{c}$for which such an intrinsic bar involution exists. Representation Theory of the American Mathematical Society 09/2014; 19(8). DOI:10.1090/ert/469 • Source ##### Article: Integral structures in the$p$-adic holomorphic discrete series [Hide abstract] ABSTRACT: For a local non-Archimedean field$K$we construct${\rm GL}_{d+1}(K)$-equivariant coherent sheaves${\mathcal V}_{{\mathcal O}_K}$on the formal${\mathcal O}_K$-scheme${\mathfrak X}$underlying the symmetric space$X$over$K$of dimension$d$. These${\mathcal V}_{{\mathcal O}_K}$are${\mathcal O}_K$-lattices in (the sheaf version of) the holomorphic discrete series representations (in$K$-vector spaces) of${\rm GL}_{d+1}(K)$as defined by P. Schneider \cite{schn}. We prove that the cohomology$H^t({\mathfrak X},{\mathcal V}_{{\mathcal O}_K})$vanishes for$t>0$, for${\mathcal V}_{{\mathcal O}_K}$in a certain subclass. The proof is related to the other main topic of this paper: over a finite field$k$, the study of the cohomology of vector bundles on the natural normal crossings compactification$Y$of the Deligne-Lusztig variety$Y^0$for${\rm GL}_{d+1}/k$(so$Y^0$is the open subscheme of${\mathbb P}_k^d$obtained by deleting all its$k$-rational hyperplanes). Representation Theory of the American Mathematical Society 08/2014; DOI:10.1090/S1088-4165-05-00259-1 • Source ##### Article: On the character of certain modular irreducible representations [Hide abstract] ABSTRACT: Let G be an almost simple, simply connected algebraic group over an algebraically closed field of characteristic p>0. In this paper we restate our conjecture from 1979 on the characters of irreducible modular representations of G so that it is now directly applicable to any dominant highest weight. Representation Theory of the American Mathematical Society 07/2014; 19(2). DOI:10.1090/S1088-4165-2015-00463-7 • ##### Article: On the theta correspondence for$(\mathrm {GSp}(4), \mathrm {GSO}(4,2))$and Shalika periods Representation Theory of the American Mathematical Society 04/2014; 18(3):28-87. DOI:10.1090/S1088-4165-2014-00451-5 • Source ##### Article: Evaluating Characteristic Functions of Character Sheaves at Unipotent Elements [Hide abstract] ABSTRACT: Assume$\mathbf{G}$is a connected reductive algebraic group defined over an algebraic closure$\mathbb{K} = \overline{\mathbb{F}}_p$of the finite field of prime order$p>0$. Furthermore, assume that$F : \mathbf{G} \to \mathbf{G}$is a Frobenius endomorphism of$\mathbf{G}$. In this article we give a formula for the value of any$F$-stable character sheaf of$\mathbf{G}$at a unipotent element. This formula is expressed in terms of class functions of$\mathbf{G}^F$which are supported on a single unipotent class of$\mathbf{G}$. In general these functions are not determined, however we give an expression for these functions under the assumption that$Z(\mathbf{G})$is connected,$\mathbf{G}/Z(\mathbf{G})$is simple and$p$is a good prime for$\mathbf{G}$. In this case our formula is completely explicit. Representation Theory of the American Mathematical Society 03/2014; 18(10). DOI:10.1090/S1088-4165-2014-00457-6 • Source ##### Article: Unipotent representations as a categorical centre [Hide abstract] ABSTRACT: Let G(F_q) be the group of rational points of a split connected reductive group G defined over the finite field F_q. In this paper we show that the category of representations of G(F_q) which are finite direct sums of unipotent representations in a fixed two-sided cell is equivalent to the centre of a certain monoidal category of sheaves on the product of two copies of the flag manifold of G. Representation Theory of the American Mathematical Society 01/2014; 19(9). DOI:10.1090/ert/468 • Source ##### Article: Geometric local theta correspondence for dual reductive pairs of type II at the Iwahori level [Hide abstract] ABSTRACT: In this paper we are interested in the geometric local theta correspondence at the Iwahori level for dual reductive pairs$(G,H)$of type II over a non-Archimedean field of characteristic$p\neq 2$in the framework of the geometric Langlands program. We consider the geometric version of the$I_{H}\times I_{G}$-invariants of the Weil representation$\mathcal{S}^{I_{H}\times I_{G}}$as a bimodule under the of action Iwahori-Hecke algebras$\mathcal{H}_{I_{G}}$and$\mathcal{H}_{I_{H}}$and we give some partial geometric description of the corresponding category under the action of Hecke functors. We also define geometric Jacquet functors for any connected reductive group$G$at the Iwahori level and we show that they commute with the Hecke action of the$\mathcal{H}_{I_{L}}$-subelgebra of$\mathcal{H}_{I_{G}}$for a Levi subgroup$L\$.
Representation Theory of the American Mathematical Society 10/2013; 17(21). DOI:10.1090/S1088-4165-2013-00448-X
• ##### Article: The Capelli identity for Grassmann manifolds
[Hide abstract]
ABSTRACT: The column space of a real n × k matrix x of rank k is a k-plane. Thus we get a map from the space X of such matrices to the Grassmannian G of k-planes in Rn, and hence a GLn-equivariant isomorphism We consider the On × GLk-invariant differential operator C On X given by By the above isomorphism, C defines an On-invariant operator on G. Since G is a symmetric space for On, the irreducible On-submodules of C∞ (G) have multiplicity 1; thus, On-invariant operators act by scalars on these submodules. Our main result determines these scalars for a general class of such operators including C. This answers a question raised by Howe and Lee and also gives new Capelli-type identities for the orthogonal Lie algebra.
Representation Theory of the American Mathematical Society 06/2013; 17(1). DOI:10.1090/S1088-4165-2013-00434-X
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##### Article: Quantum supergroups II. Canonical basis
[Hide abstract]
ABSTRACT: Following Kashiwara's algebraic approach, we construct crystal bases and canonical bases for quantum supergroups with no isotropic odd roots and for their integrable modules.
Representation Theory of the American Mathematical Society 04/2013; 18(9). DOI:10.1090/S1088-4165-2014-00453-9
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##### Article: Distinguished conjugacy classes and elliptic Weyl group elements
[Hide abstract]
ABSTRACT: We define and study a correspondence between the set of distinguished G^0-conjugacy classes in a fixed connected component of a reductive group G (with G^0 almost simple) and the set of (twisted) elliptic conjugacy classes in the Weyl group. We also prove a homogeneity property related to this correspondence.
Representation Theory of the American Mathematical Society 04/2013; 18(1). DOI:10.1090/S1088-4165-2014-00455-2