A Specht filtration of an induced Specht module

Andrew Mathas

Abstract

Let \(\mathscr{H}_n\) be a (degenerate or non-degenerate) Hecke algebra of type \(G(l,1,n)\), defined over a commutative ring \(R\) with \(1\), and let \(S(\mu)\) be a Specht module for \(\mathscr{H}_n\). This paper shows that the induced Specht module \(S(\mu)\otimes_{\mathscr{H}_n}\mathscr{H}_{n+1}\) has an explicit Specht filtration.

Keywords: Hecke algebras, Specht modules, induction.

AMS Subject Classification: Primary 20C08; secondary 20C30, 05E10.