PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Nigel Higson, Stephanie Zerby.

Title:Generalized exponents, family algebras and representations with simple spectrum
Seminar:Department of Mathematics Colloquium
Speaker:Alexandre Kirillov, University of Pennsylvania
Abstract:
In representation theory there are several "evergreen" subjects such as symmetric functions, multiplicity of weights, tensor invariants, etc. One of such subject, less known among non-experts, is the theory of generalized exponents, introduced by Kostant half a century ago and still resisting all endeavors towards explicit computation. The collection of generalized exponents is the so-called q-analogue of the multiplicity of the zero weight. As one possible approach to the problem, I introduced in 2000 the notion of a family algebra associated to any irreducible representation of a simple Lie algebra. The structure of these algebras is closely related to generalized exponents. For representations with simple spectrum, family algebras have relatively a simple structure, and this allows to compute explicitly generalized exponents for many irreducible representations.

Room Reservation Information

Room Number:MB114
Date:01 / 31 / 2013
Time:03:35pm - 04:25pm