Covariants of the symmetric group and its analogs in Weyl algebras
type: Item
instance of: scholarly article
title: Covariants of the symmetric group and its analogs in Weyl algebras
zbMATH Open document ID: 0821.20002
DOI: 10.1007/BF01077957
author: Igor Pak
author: A. A. Kirillov
publication date: 1992-06-25T00:00:00Z
review text: We call the algebra \(E(V)=S(V)\otimes\Lambda(V)\), \(S(V)\) the symmetric algebra, \(E(V)\) the exterior algebra for a given \(G\)-module \(V\), the Weyl algebra. For the Poincaré series \(P^ G_ \pi(t,s)=\sum_{p,q} m_{p,q} (\pi) t^ p s^ q\) (where \(\pi\) is an irreducible representation of the group \(G\), \(m_{p,q}(\pi)\) is the multiplicity of it in \(E^{p,q} (V)=S^ p(V)\otimes\Lambda^ q(V)\)), a superanalog of the expression of \(P^ G_ \pi(t,0)\) in the cases where \(V=\mathbb{R}^ n\) and \(G\) is either the symmetric group \(S(n)\) or \(C(n)=S(n)\times Z^ n_ 2\) is proved and a combinatorial interpretation of the multiplicities is given.
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 16W55
zbMATH DE Number: 6309
zbMATH Keywords: symmetric algebras
zbMATH Keywords: exterior algebras
zbMATH Keywords: Weyl algebras
zbMATH Keywords: Poincaré series
zbMATH Keywords: irreducible representations
zbMATH Keywords: superanalogs
zbMATH Keywords: symmetric groups
zbMATH Keywords: multiplicities
MaRDI profile type: Publication
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published in: Functional Analysis and Its Applications
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description: scientific article; zbMATH DE number 6309