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
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