2018/01/28 by Futorny, Vyacheslav, Grantcharov, Dimitar, Ramírez, Luis Enrique +1 · 1 citation
#16G99 #17B10 #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1801.09316
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 \mathfrakgl (n) and the finite W-algebras of type A.