On the symmetric Gelfand pair (ℋn ×ℋn−1,diag(ℋn−1))

Abstract

We show that the [Formula: see text]-conjugacy classes of [Formula: see text] where [Formula: see text] is the hyperoctahedral group on [Formula: see text] elements, are indexed by marked bipartitions of [Formula: see text] This will lead us to prove that [Formula: see text] is a symmetric Gelfand pair and that the induced representation [Formula: see text] is multiplicity free.