Abstract Young representations for Coxeter groups of type D

Young (briefly: AY) representations are Coxeter group representations which carry an extended Young form. These representations appear in a new axiomatic approach to the representation theory of Coxeter groups. While AY representations for Coxeter groups of types A and B are well understood, little is known about type D. We introduce D-Young tableaux and study minimal AY representations associated with them. The main result is a decomposition rule for the AY representations which are induced from S, into D-n. The proof of this rule involves a combinatorial bijection together with theorems from complex analysis. (C) 2008 Elsevier Inc. All rights reserved.