On $C$-bases, partition pairs and filtrations for induced or restricted Specht modules

TL;DR

This paper develops explicit Specht filtrations for induced and restricted modules in Hecke algebras of symmetric groups using $C$-bases, linking these bases to pairs of partitions, advancing understanding of module structures.

Contribution

It introduces new explicit Specht filtrations via $C$-bases and connects these bases to partition pairs, offering a novel approach in the representation theory of Hecke algebras.

Findings

Explicit Specht filtrations for induced modules

Explicit Specht filtrations for restricted modules

Link between $C$-bases and partition pairs

Abstract

We obtain alternative explicit Specht filtrations for the induced and the restricted Specht modules in the Hecke algebra of the symmetric group (defined over the ring $A=\mathbb Z[q^{1/2},q^{-1/2}]$ where $q$ is an indeterminate) using $C$-bases for these modules. Moreover, we provide a link between a certain $C$-basis for the induced Specht module and the notion of pairs of partitions.