Seminar in Algebra, Lie Theory, and Geometry

Pablo Zadunaisky

(Jacobs University Bremen)

"Gelfand-Tsetlin realization of gl(n) modules"

Date: Wed, May 8, 2019
Time: 15:00
Place: Seminar Room (120), Research I

Abstract: The enveloping algebra U of gl(n) contains a very large commutative subalgebra, known as the Gelfand-Tsetlin subalgebra. A GT module over gl(n) is a finitely generated module on which the Gelfand-Tsetlin subalgebra acts in a locally finite way. One expects generic objects of the category of GT-modules to have a combinatorial description similar to that given by Gelfand and Tsetlin for finite dimensional simple representations. Inspired by this idea, we describe several natural objects of this category in this way, and in particular explore the possibility of giving such a presentation for Verma modules and other classical representations of gl(n).