Relations between the minors of a generic matrix

Abstract

It is well-known that the Plucker relations generate the ideal of relations of the maximal minors of a generic m x n matrix. In this paper we discuss the relations of t-minors for t < min(m, n). We will exhibit minimal relations in degrees 2 (non-Plucker in general) and 3, and give some evidence for our conjecture that we have found the generating system of the ideal of relations. The approach is through the representation theory of the general linear group. (C) 2013 Elsevier Inc. All rights reserved.