On a relation between the basic representation of the affine Lie algebra $\widehat\sl$ and a Schur--Weyl representation of the infinite symmetric group

We prove that there is a natural grading-preserving isomorphism of $\sl$-modules between the basic module of the affine Lie algebra $\widehat\sl$ (with the homogeneous grading) and a Schur--Weyl module of the infinite symmetric group $\sinf$ with a grading defined through the combinatorial notion of...

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Bibliographic Details
Main Authors Tsilevich, Natalia, Vershik, Anatoly
Format Journal Article
LanguageEnglish
Published 06.03.2014
Subjects
Mathematics - Representation Theory
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Summary:We prove that there is a natural grading-preserving isomorphism of $\sl$-modules between the basic module of the affine Lie algebra $\widehat\sl$ (with the homogeneous grading) and a Schur--Weyl module of the infinite symmetric group $\sinf$ with a grading defined through the combinatorial notion of the major index of a Young tableau, and study the properties of this isomorphism. The results reveal new and deep interrelations between the representation theory of $\widehat\sl$ and the Virasoro algebra on the one hand, and the representation theory of $\sinf$ and the related combinatorics on the other hand.
DOI:10.48550/arxiv.1403.1558