Representation Theory of the American Mathematical Society (Represent Theor)
Journal description
This electroniconly journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content.
Current impact factor: 0.73
Impact Factor Rankings
2015 Impact Factor  Available summer 2016 

2014 Impact Factor  0.732 
2013 Impact Factor  0.475 
Additional details
5year impact  0.00 

Cited halflife  7.30 
Immediacy index  0.22 
Eigenfactor  0.00 
Article influence  0.00 
Website  Representation Theory website 
Other titles  Representation theory 
ISSN  10884165 
OCLC  34602921 
Material type  Document, Internet resource 
Document type  Internet Resource, Computer File, Journal / Magazine / Newspaper 
Publisher details
 Preprint
 Author can archive a preprint version
 Postprint
 Author can archive a postprint 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
 Noncommercial
 Eligible UK authors may deposit in OpenDepot
 Classificationgreen
Publications in this journal
 Representation Theory of the American Mathematical Society 10/2015; 19(10):236262. DOI:10.1090/ert/466
 Representation Theory of the American Mathematical Society 10/2015; 19(7):167185. 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):12. DOI:10.1090/S108841652015004601  [Show abstract] [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 2group. 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  [Show abstract] [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  [Show abstract] [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):341360. DOI:10.1090/S108841652014004588  [Show abstract] [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 KacMoody 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  [Show abstract] [Hide abstract]
ABSTRACT: For a local nonArchimedean 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 DeligneLusztig 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/S1088416505002591  [Show abstract] [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/S108841652015004637 
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):2887. DOI:10.1090/S108841652014004515  [Show abstract] [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/S108841652014004576  [Show abstract] [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 twosided 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 
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 nonArchimedean 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 IwahoriHecke 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/S10884165201300448X  [Show abstract] [Hide abstract]
ABSTRACT: The column space of a real n × k matrix x of rank k is a kplane. Thus we get a map from the space X of such matrices to the Grassmannian G of kplanes in Rn, and hence a GLnequivariant isomorphism We consider the On × GLkinvariant differential operator C On X given by By the above isomorphism, C defines an Oninvariant operator on G. Since G is a symmetric space for On, the irreducible Onsubmodules of C∞ (G) have multiplicity 1; thus, Oninvariant 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 Capellitype identities for the orthogonal Lie algebra.Representation Theory of the American Mathematical Society 06/2013; 17(1). DOI:10.1090/S10884165201300434X  [Show abstract] [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/S108841652014004539  [Show abstract] [Hide abstract]
ABSTRACT: We define and study a correspondence between the set of distinguished G^0conjugacy 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/S108841652014004552
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