You are here

Georgia Benkart

Georgia Benkart is Professor of Mathematics at the University of Wisconsin, Madison. She received her Ph.D. from Yale University, the 29th of Nathan Jacobson's 33 students. Her main research interests are Lie algebras and groups, representation theory, and combinatorics. She has been a contributor to the classification of simple Lie algebras of prime characteristic and of infinite-dimensional Lie algebras ([1-3]) and to combinatorial representation theory ([4-5]).

Her January 1994 AMS-MAA Invited Hour Address, "A Tale of Two Groups," told in Dickensian fashion the story begun 80 years ago by Issai Schur tying the knot between the symmetric groups and the general linear groups of invertible matrices. It's a old story but nevertheless a very timely one with many new developments and applications to the theory of symmetric functions, representation theory, knot theory, invariant theory, combinatorics, and particle physics. An expanded version of this talk was the basis of her 10 lectures at Holiday Symposium at New Mexico State University in December 1992.

Some of her latest work involves some algebras she and T. Roby invented called "down-up algebras" [6]. These algebras have connections with all sorts of things in combinatorics, physics, and algebra. In 1987 she received the University of Wisconsin's highest prize for distinguished teaching. She has had 14 graduate students complete their doctoral degrees under her direction. She has been an editor of Journal of Algebra since 1991 and serves on the editorial board of the AMS' Surveys and Monographs series.

1. Rank one Lie algebras (with J.M. Osborn), Annals of Math. 119
(1984) 437-463.

2. Contributions to the classification of simple modular Lie algebras,
(with J.M. Osborn and H. Strade), Trans. Amer. Math. Soc. 341 (1994),

3. Lie algebras graded by finite root systems and intersection matrix
algebras (with E. Zelmanov), Inventiones Math. 126 (1996), 1-45.

4. Commuting actions: A tale of two groups, Contemporary Math. Amer. Math.
Soc. 194 (1996) 1-46.

5. Crystal bases for the quantum superalgebra U_q(gl(m,n)),
(with S.-J. Kang and M. Kashiwara), Journal of Amer. Math. Soc. (2000).

6. Down-up algebras (with T. Roby), Journal of Algebra, 209 (1998), 305-344.