Mathematical Sciences Colloquium

Graded Hecke algebras are infinite-dimensional noncommutative algebras which can be defined using reflection groups, such as the symmetries of a 2n-gon or an icosahedron. Not only did certain of these algebras arise originally in the work of G. Lusztig on the representation theory of p-adic groups, they are also of interest for their own sake, in part due to recent connections to Yang's n-particle problem in physics. This talk will include results on the classification of representations of graded Hecke algebras, as well as an unexpected result related to a number theoretic conjecture on the existence of Whittaker models .