CU Algebraic Lie Theory Seminar

P-kernels and IC bases

Richard Green, CU

Abstract

This talk will introduce the notion of a $P$-kernel, due to R.P. Stanley. I will explain how $P$-kernels can regarded as an abstraction of Kazhdan--Lusztig theory in which the collection of all Kazhdan--Lusztig polynomials is treated as a single combinatorial object in terms of an incidence algebra. The relationship between $P$-kernels and IC ("Intersection Cohomology") bases will also be discussed.