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arXiv · 1611.07908

Combinatorial construction of Gelfand-Tsetlin modules for $\mathfrak{gl}_n$

Vyacheslav Futorny·Luis Enrique Ramirez·Jian Zhang
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Abstract

We propose a new effective method of constructing explicitly Gelfand -Tsetlin modules for $\mathfrak{gl}_n$. We obtain a large family of simple modules that have a basis consisting of Gelfand-Tsetlin tableaux, the action of the Lie algebra is given by the Gelfand-Tsetlin formulas and with all Gelfand-Tsetlin multiplicities equal $1$. As an application of our construction we prove necessary and sufficient condition for the Gelfand and Graev's continuation construction to define a module which was conjectured by Lemire and Patera.

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BibTeXRIS

Vyacheslav Futorny, Luis Enrique Ramirez, Jian Zhang. 2016-11-23. Combinatorial construction of Gelfand-Tsetlin modules for $\mathfrak{gl}_n$. https://arxiv.org/abs/1611.07908

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