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.
"Infinitedimensional Weight Representations of Lie
Algebras"
Abstract:
In the early 20th century H. Weyl classified all finitedimensional
representations of the classical Lie algebras in terms of the socalled
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 infinitedimensional
analog of Weyl's result. Using a combination of algebrogeometric methods and
noncommutative localization constructions, O. Mathieu classified all simple
infinitedimensional 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.
