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arXiv · 1801.09316

Gelfand-Tsetlin Theory for Rational Galois Algebras

Vyacheslav Futorny·Dimitar Grantcharov·Luis Enrique Ramírez·Pablo Zadunaisky
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Abstract

In the present paper we study Gelfand-Tsetlin modules defined in terms of BGG differential operators. The structure of these modules is described with the aid of the Postnikov-Stanley polynomials introduced in [PS09]. These polynomials are used to identify the action of the Gelfand-Tsetlin subalgebra on the BGG operators. We also provide explicit bases of the corresponding Gelfand-Tsetlin modules and prove a simplicity criterion for these modules. The results hold for modules defined over standard Galois orders of type $A$ - a large class of rings that include the universal enveloping algebra of $\mathfrak{gl} (n)$ and the finite $W$-algebras of type $A$.

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BibTeXRIS

Vyacheslav Futorny, Dimitar Grantcharov, Luis Enrique Ramírez, Pablo Zadunaisky. 2018-01-28. Gelfand-Tsetlin Theory for Rational Galois Algebras. https://arxiv.org/abs/1801.09316

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