A generalization of Carter-Payne homomorphisms

TL;DR

This paper generalizes Carter-Payne homomorphisms to graded Specht modules of quiver Hecke algebras of type A, extending classical symmetric group results using advanced algebraic methods.

Contribution

It introduces a comprehensive construction of graded homomorphisms between Specht modules differing by specific removable node sets, broadening the scope of Carter-Payne theory.

Findings

Constructed graded homomorphisms for a broad class of Specht modules.

Extended classical Carter-Payne results to quiver Hecke algebra context.

Provided explicit methods for module homomorphism construction.

Abstract

We construct graded homomorphisms between Specht modules of quiver Hecke algebras of type A that differ by an ``$e$-small'' partition-shaped removable set of nodes by expanding on methods by Lyle and Mathas. Our main result constitutes a full generalization of the classical result by Carter and Payne for Specht modules of the symmetric group.