A Specht Filtration of Permutation Modules Over KLR Algebras

TL;DR

This paper constructs Specht filtrations of permutation modules over KLR algebras in type A, providing new structural insights and generalizations for modules indexed by hook and arbitrary partitions.

Contribution

It introduces Specht filtrations for permutation modules in affine type A and extends to arbitrary partitions in the linear quiver case, advancing module theory in KLR algebras.

Findings

Specht filtration constructed for permutation modules in affine type A

Generalized Specht filtration developed for modules indexed by any partition in linear quiver case

Provides new tools for understanding module structure over KLR algebras

Abstract

In type A, Kleshchev-Ram-Mathas realize Specht modules as quotient of Permutation modules, in this paper, we construct a Specht filtration of Permutation modules indexed by hook partition in affine type A; and construct a generalized Specht filtration of Permutation modules indexed by any partition in linear quiver case.