2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106149In this paper we study the branching problems for Hecke algebra $\H(D_n)$ of type $D_n$. We explicitly describe the decompositions of the socle of the restriction of each irreducible $\H(D_n)$-representation to $\H(D_{n-1})$ 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.Representation TheoryCombinatoricstext