Partitions of single exterior type

TL;DR

This paper characterizes specific irreducible representations of the general linear group related to exterior powers, connecting them to minimal relations in matrix minors, and identifies those with multiplicity one.

Contribution

It provides a complete characterization of irreducible representations with multiplicity one in the context of exterior powers, linking them to partitions of single exterior type.

Findings

Identifies irreducible representations with multiplicity one in Schur modules of exterior powers.

Shows minimal relations are exactly those from partitions of single exterior type.

Connects representation theory with algebraic relations of matrix minors.

Abstract

We characterize the irreducible representations of the general linear group GL(V) that have multiplicity 1 in the direct sum of all Schur modules of a given exterior power of V. These have come up in connection with the relations of the lower order minors of a generic matrix. We show that the minimal relations conjectured by Bruns, Conca and Varbaro are exactly those coming from partitions of single exterior type.