Nat Thiem (CU) An introduction to combinatorial representation theory
Sep. 06, 2007 2pm (MATH 350)
Lie Theory
Richard Green (CU)
X
Kazhdan--Lusztig polynomials are subtle objects that arise naturally in the context of Hecke algebras associated to Coxeter groups. I will discuss how methods from the theory of diagram algebras may be used to help compute these polynomials.
Diagram algebras and Kazhdan-Lusztig polynomials
Sep. 20, 2007 2pm (MATH 350)
Lie Theory
Nat Thiem (CU)
X
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.
Diagram algebras and Kazhdan-Lusztig polynomials