Karel Casteels: Quantum Matrices by Paths

Abstract

Abstract: The quantized coordinate ring of m x n matrices (AKA quantum matrices) and its prime and primitive ideals are usually studied using algebraic methods. In this talk, I will show that in fact one can define this algebra combinatorially, using the set of directed paths in a certain graph. I'll then discuss how this viewpoint gives a purely combinatorial understanding of some important prime and primitive ideals.