QUASI-DETERMINANTS AND q-COMMUTING MINORS

摘要

Abstract. We present two new proofs of the q-commuting property holdingnamong certain pairs of quantumminors of a q-genericmatrix. The first uses elementarynquasi-determinantal arithmetic; the second involves paths in a directed graph.Together,nthey indicate ameans to build themulti-homogeneous coordinate rings of flag varietiesnin other non-commutative settings.