UTA Department of Mathematics

Metroplex Algebraic Geometry, Algebra and Number Theory (AGANT) Seminar,
a joint venture of   UNT,   UTA   and   TCU

Date/Time/Room: Friday (9/19/2008) at 4:00 pm in 304 Pickard Hall

Speaker: Dr. Dimitar Grantcharov, Assistant Professor
Department of Mathematics, University of Texas at Arlington.

"Infinite-dimensional Weight Representations of Lie Algebras"

Abstract: In the early 20th century H. Weyl classified all finite-dimensional representations of the classical Lie algebras in terms of the so-called character formula. Following work of G. Benkart, D. Britten, V. Futorny, F. Lemire, A. Joseph and others, in 2000, O. Mathieu achieved a major breakthrough in the representation theory by obtaining an infinite-dimensional analog of Weyl's result. Using a combination of algebro-geometric methods and non-commutative localization constructions, O. Mathieu classified all simple infinite-dimensional weight representations of the classical Lie algebras. In this talk we will discuss some recent results related to the theory of weight representations. These results are a part of an ongoing joint project of the speaker with V. Serganova.