Quasi-Commuting Families of Quantum Minors

Abstract

We produce neccessary and sufficient conditions for pairs of quantum minors in the quantized coordinate algebra ${\mathbb{C}}_q[Ma{t}_{k\times m}]$ to quasi-commute. In addition we study the combinatorics of maximal (by inclusion) families of pairwise quasi-commuting quantum minors.

Latex; 18 pages, 4 figures