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
|Date:||01 / 31 / 2013|
|Time:||03:35pm - 04:25pm|