CU Algebraic Lie Theory Seminar

CU Algebraic Lie Theory Seminar
The Geometric Hecke algebra Rahbar Virk, CU
October 11, 2011 Math 350 2-3pm	Abstract A pervading tenet in mathematics is that to study an `object' one should study the `functions' on the object. I will explain the meaning of this with some very elementary examples (involving sets and functions on them). In particular, I will show that several (= at least 2) algebras of interest in combinatorics and representation theory arise via such set-theoretic models. I will then explain, using the particular example of the Hecke algebra, how to upgrade such a `function theory' to give a geometric/categorical realization of the algebra. The upshot: several a priori deep properties (including the definition) of the Hecke algebra and Kazhdan-Lusztig polynomials will be seen to be `obvious'.

The Geometric Hecke algebra

Rahbar Virk, CU

October 11, 2011

Math 350

2-3pm

Abstract

A pervading tenet in mathematics is that to study an `object' one should study the `functions' on the object. I will explain the meaning of this with some very elementary examples (involving sets and functions on them). In particular, I will show that several (= at least 2) algebras of interest in combinatorics and representation theory arise via such set-theoretic models. I will then explain, using the particular example of the Hecke algebra, how to upgrade such a `function theory' to give a geometric/categorical realization of the algebra. The upshot: several a priori deep properties (including the definition) of the Hecke algebra and Kazhdan-Lusztig polynomials will be seen to be `obvious'.