2011/11/30 by Bruns, Winfried, Conca, Aldo, Varbaro, Matteo
#13A50 #14L30 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1111.7263
It is well-known that the Plücker relations generate the ideal of relations of the maximal minors of a generic matrix. In this paper we discuss the relations between minors of a (non-maximal) fixed size. We will exhibit minimal relations in degrees 2 (non-Plücker 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.