Gelfand-Tsetlin modules for gl(n,m)

Vyacheslav Futorny; Vera Serganova; Jian Zhang

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arXiv · 2001.06112

Gelfand-Tsetlin modules for gl(n,m)

Vyacheslav Futorny·Vera Serganova·Jian Zhang

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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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BibTeX RIS

Vyacheslav Futorny, Vera Serganova, Jian Zhang. 2020-01-16. Gelfand-Tsetlin modules for gl(n,m). https://arxiv.org/abs/2001.06112

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