Cyclotomic Carter-Payne homomorphisms

TL;DR

This paper introduces a new family of homomorphisms between graded Specht modules in quiver Hecke algebras of type A, extending and generalizing classical Carter-Payne homomorphisms for symmetric groups.

Contribution

It constructs a novel family of homomorphisms in the context of quiver Hecke algebras, broadening the understanding of module homomorphisms beyond classical cases.

Findings

New homomorphisms constructed for graded Specht modules

Maps exhibit similarities and differences with classical Carter-Payne homomorphisms

Enhances the algebraic understanding of quiver Hecke algebra modules

Abstract

We construct a new family of homomorphisms between (graded) Specht modules of the quiver Hecke algebras of type A. These maps have many similarities with the homomorphisms constructed by Carter and Payne in the special case of the symmetric groups, although the maps that we obtain are both more and less general than these.