Action of intertwining operators on pseudospherical K-types

Abstract

In this paper, we give a concrete description of the two-fold cover of a simply connected, split real reductive group and its maximal compact subgroup as Chevalley groups. We define a representation of the maximal compact subgroup called pseudospherical representation, it appears with multiplicity one in the principal series representation. We introduce a family of canonically defined intertwining operators and compute the action of them on pseudospherical K-types, obtaining explicit formulas of the Harish-Chandra c-function.