# 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

2016 Impact Factor Available summer 2017 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: fgh dh

No preview · Article · Dec 2016 · Representation Theory of the American Mathematical Society
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##### Article: Regular Functions of Symplectic Spherical Nilpotent Orbits and their Quantizations
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ABSTRACT: We study the ring of regular functions of classical spherical orbits $R(\mathcal{O})$ for $G = Sp(2n,\mathbb{C})$. In particular, treating $G$ as a real Lie group with maximal compact subgroup $K$, we focus on a quantization model of $\mathcal{O}$ when $\mathcal{O}$ is the nilpotent orbit $(2^{2p}1^{2q})$. With this model, we verify a conjecture by McGovern and another conjecture by Achar and Sommers for such orbits. Assuming the results in [Barbasch 2008], we will also verify the Achar-Sommers conjecture for a larger class of nilpotent orbits.
Preview · Article · Nov 2015 · Representation Theory of the American Mathematical Society
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##### Article: L’involution de Zelevinski modulo $\ell Preview · Article · Oct 2015 · Representation Theory of the American Mathematical Society • Source ##### Article: Classification of discrete series by minimal$K$-type Preview · Article · Oct 2015 · Representation Theory of the American Mathematical Society • Source ##### Article: Cuspidal representations of reductive p-adic groups are relatively injective and projective [Hide abstract] ABSTRACT: Cuspidal representations of a reductive p-adic group G over a field of characteristic different from p are relatively injective and projective with respect to extensions that split by a U-equivariant linear map for any subgroup U that is compact modulo the centre. The category of smooth representations over a field whose characteristic does not divide the pro-order of G is the product of the subcategories of cuspidal representations and of subrepresentations of direct sums of parabolically induced representations. Preview · Article · Apr 2015 · Representation Theory of the American Mathematical Society • ##### Article: Corrections to: “On the$\mathfrak n$-cohomology of limits of discrete series representations” No preview · Article · Jan 2015 · Representation Theory of the American Mathematical Society • 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. Preview · Article · Jan 2015 · Representation Theory of the American Mathematical Society • 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,) Preview · Article · Nov 2014 · Representation Theory of the American Mathematical Society • 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. Preview · Article · Oct 2014 · Representation Theory of the American Mathematical Society • Source ##### Article: Dimensions of some locally analytic representations [Hide abstract] ABSTRACT: Let$G$be the group of points of a split reductive group over a finite extension of${\mathbb Q}_p$. In this paper, we compute the dimensions of certain classes of locally analytic$G$-representations. This includes principal series representations and certain representations coming from homogeneous line bundles on$p$-adic symmetric spaces. As an application, we compute the dimensions in Colmez' unitary principal series of${\rm GL}_2({\mathbb Q}_p)$. Preview · Article · Sep 2014 · Representation Theory of the American Mathematical Society • Source ##### Article: The bar involution for quantum symmetric pairs [Hide abstract] ABSTRACT: We construct a bar involution for quantum symmetric pair coideal subalgebras$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}$for which such an intrinsic bar involution exists. Preview · Article · Sep 2014 · Representation Theory of the American Mathematical Society • Source ##### Article: Integral structures in the$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$-rational hyperplanes). Preview · Article · Aug 2014 · Representation Theory of the American Mathematical Society • Source ##### Article: On the character of certain modular irreducible representations [Hide abstract] ABSTRACT: Let G be an almost simple, simply connected algebraic group over an algebraically closed field of characteristic p>0. In this paper we restate our conjecture from 1979 on the characters of irreducible modular representations of G so that it is now directly applicable to any dominant highest weight. Preview · Article · Jul 2014 · Representation Theory of the American Mathematical Society • Source ##### Article: On the theta correspondence for$(\mathrm {GSp}(4), \mathrm {GSO}(4,2))$and Shalika periods [Hide abstract] ABSTRACT: We consider both local and global theta correspondences for GSp(4) and GSO(4,2). Because of the accidental isomorphism PGSO(4,2) similar or equal to PGU(2,2), these correspondences give rise to those between GSp(4) and GU(2,2) for representations with trivial central characters. In the global case, using this relation, we characterize representations with trivial central character, which have Shalika period on GU(2, 2) by theta correspondences. Moreover, in the local case, we consider a similar relationship for irreducible admissible representations without an assumption on the central character. Preview · Article · Apr 2014 · Representation Theory of the American Mathematical Society • Source ##### Article: Evaluating Characteristic Functions of Character Sheaves at Unipotent Elements [Hide abstract] ABSTRACT: Assume$\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.
Preview · Article · Mar 2014 · Representation Theory of the American Mathematical Society
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##### Article: Unipotent representations as a categorical centre
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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.
Preview · Article · Jan 2014 · Representation Theory of the American Mathematical Society