Gelfand-Tsetlin modules for gl(n,m)

2020/01/16 by Vyacheslav Futorny, Futorny, Vyacheslav, Vera Serganova +3 · 1 citation
Mathematics · Computer Science · #Advanced Algebra and Geometry #Finite Group Theory Research #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.2001.06112

Abstract

We address the problem of classifying of irreducible Gelfand-Tsetlin modules for gl(m|n) and show that it reduces to the classification of Gelfand-Tsetlin modules for the even part. We also give an explicit tableaux construction and the irreducibility criterion for the class of quasi typical and quasi covariant Gelfand-Tsetlin modules which includes all essentially typical and covariant tensor finite dimensional modules. In the quasi typical case new irreducible representations are infinite dimensional gl(m|n)-modules which are isomorphic to the parabolically induced (Kac) modules.

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