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.
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