A Specht filtration of an induced Specht module

TL;DR

This paper demonstrates that the induced Specht module for Hecke algebras of type G(ℓ,1,n) admits an explicit Specht filtration, providing structural insights into module induction.

Contribution

It establishes an explicit Specht filtration for induced Specht modules in Hecke algebras of type G(ℓ,1,n), advancing understanding of their module structure.

Findings

Explicit Specht filtration constructed for induced modules.

Provides structural understanding of module induction in Hecke algebras.

Enhances tools for studying representations of Hecke algebras.

Abstract

Let $\H_n$ be a (degenerate or non-degenerate) Hecke algebra of type $G(\ell,1,n)$, defined over a commutative ring $R$ with one, and let $S(\bmu)$ be a Specht module for $\H_n$. This paper shows that the induced Specht module $S(\bmu)\otimes_{\H_n}\H_{n+1}$ has an explicit Specht filtration.