Texas A&M University, Department of
Mathematics, 216 Milner Hall, 3rd of November 2004, 3:00-3:50
Groups and Dynamics Seminar
Reflection groups
and graded Hecke algebras
Sarah Witherspoon of Texas A&M
University
Given a vector space V and a finite subgroup G of the general linear
group GL(V), Drinfel'd defined a graded Hecke algebra. These algebras
have been studied for particular types of groups by many people
including Lusztig (real reflection groups), Ram-Shepler (complex
reflection groups), and Etingof-Ginzburg (symplectic reflection
groups). Technically, a graded Hecke algebra is a deformation of a
crossed product of the polynomial ring S(V) with the group G. This is
the point of view we will take in this talk, where we will introduce
and motivate all of the concepts mentioned above, and give a
generalization of graded Hecke algebras that is potentially of
interest.