Corners and fundamental corners for the groups Spin(n,1)

Abstract

We study corners and fundamental corners of the irreducible representations of the groups G=Spin(n,1) that are not elementary, i.e. that are equivalent to subquotients of reducible nonunitary principal series representations. For even n we obtain results in a way analogous to the results in [10] for the groups SU(n,1). Especially, we again get a bijection between the nonelementary part ${\hat{G}}^0$ of the unitary dual $\hat{G}$ and the unitary dual $\hat{K}.$ In the case of odd n we get a bijection between ${\hat{G}}^0$ and a tru subset of $\hat{K}.$