Branching rules for Hecke Algebras of Type $D_n$

Abstract

In this paper we study the branching problems for Hecke algebra $\stackrel{˝}{(}{D}_n)$ of type $D_n$. We explicitly describe the decompositions of the socle of the restriction of each irreducible $\stackrel{˝}{(}{D}_n)$-representation to $\stackrel{˝}{(}{D}_{n-1})$ into irreducible modules by using the corresponding results for type $B$ Hecke algebras. In particular, we show that any such restrictions are always multiplicity free.