Action of Intertwining operators on pseudospherical K-types

TL;DR

This paper provides explicit formulas for intertwining operators acting on pseudospherical K-types in split real reductive groups, enhancing understanding of their representation theory and the Harish-Chandra c-function.

Contribution

It offers a concrete description of the two-fold cover of split real reductive groups and computes the action of intertwining operators on pseudospherical K-types with explicit formulas.

Findings

Explicit formulas for intertwining operators on pseudospherical K-types

Concrete description of the two-fold cover as Chevalley groups

Explicit computation of the Harish-Chandra c-function

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.