## 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.

: Primary 20C08; secondary 20C30, 05E10.

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 Monday, March 30, 2009