CU Algebraic Lie Theory Seminar

Unipotent Hecke algebras

Nat Thiem, CU

Abstract

Hecke algebras are fundamental tools that appear throughout mathematics including representation theory, number theory, geometry, and probability. In representation theory, they play an important role interpolating between groups and their combinatorics. Unipotent Hecke algebras are a family of Hecke algebras that "see" the representation theory of finite groups of Lie type but act much more like Weyl groups (Coxeter groups). Their structure varies widely, ranging from generalizations the usual Iwahori-Hecke algebra to a commutative algebra often studied in number theory. This talk will begin with a general construction of Hecke algebras and then specialize to the combinatorics of unipotent Hecke algebras.