# 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

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##### Article: On the $W$-action on $B$-sheets in positive characteristic
Representation Theory of the American Mathematical Society 03/2015; 19(3):9-23. DOI:10.1090/S1088-4165-2015-00464-9
• ##### 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
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##### Article: Borel subgroups adapted to nilpotent elements of standard Levi type
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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
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##### Article: Integral structures in the $p$-adic holomorphic discrete series
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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
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##### Article: On the character of certain modular irreducible representations
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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
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##### Article: Evaluating Characteristic Functions of Character Sheaves at Unipotent Elements
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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
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##### Article: Geometric local theta correspondence for dual reductive pairs of type II at the Iwahori level
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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
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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
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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
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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; DOI:10.1090/S1088-4165-2014-00455-2
• ##### Article: Complement to the appendix of: “On the Howe duality conjecture”
Representation Theory of the American Mathematical Society 03/2013; DOI:10.1090/S1088-4165-2013-00428-4
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##### Article: Homological approach to the Hernandez-Leclerc construction and quiver varieties
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ABSTRACT: In a previous paper the authors have attached to each Dynkin quiver an associative algebra. The definition is categorical and the algebra is used to construct desingularizations of arbitrary quiver Grassmannians. In the present paper we prove that this algebra is isomorphic to an algebra constructed by Hernandez-Leclerc defined combinatorially and used to describe certain graded Nakajima quiver varieties. This approach is used to get an explicit realization of the orbit closures of representations of Dynkin quivers as affine quotients.
Representation Theory of the American Mathematical Society 02/2013; 18(1). DOI:10.1090/S1088-4165-2014-00449-7
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##### Article: Spin polynomial functors and representations of Schur superalgebras
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ABSTRACT: We introduce categories of homogeneous strict polynomial functors, $\Pol^\I_{d,\k}$ and $\Pol^\II_{d,\k}$, defined on vector superspaces over a field $\k$ of characteristic not equal 2. These categories are related to polynomial representations of the supergroups $GL(m|n)$ and Q(n), respectively. In particular, we prove an equivalence between $\Pol^\I_{d,\k}$, $\Pol^\II_{d,\k}$ and the category of finite dimensional supermodules over the Schur superalgebra $\Sc(m|n,d)$, $\Qc(n,d)$ respectively provided $m,n \ge d$. We also discuss some aspects of Sergeev duality from the viewpoint of the category $\Pol^\II_{d,\k}$.
Representation Theory of the American Mathematical Society 01/2013; 17(20). DOI:10.1090/S1088-4165-2013-00445-4
• ##### Article: On certain elements in the Bernstein center of GL 2
Representation Theory of the American Mathematical Society 01/2013; DOI:10.1090/S1088-4165-2013-00427-2