#### Vol. 286, No. 1, 2017

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Action of intertwining operators on pseudospherical $K$-types

### Shiang Tang

Vol. 286 (2017), No. 1, 191–214
##### Abstract

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 study the representations of the maximal compact subgroups called pseudospherical representations, which appear with multiplicity one in the principal series representation. We introduce a family of canonically defined intertwining operators and compute their action on pseudospherical $K“$-types, obtaining explicit formulas of the Harish-Chandra $c$-function.

##### Keywords
pseudospherical representation, Shimura representation, intertwining operator, nonlinear real group, Gindikin–Karpelevich formula, Kubota cocycle, Chevalley groups, central extension
##### Mathematical Subject Classification 2010
Primary: 20G05, 22E50
##### Milestones
Received: 8 December 2015
Revised: 3 May 2016
Accepted: 28 May 2016
Published: 9 December 2016
##### Authors
 Shiang Tang Department of Mathematics University of Utah 155 South 1400 East, Room 233 Salt Lake City, UT 84112 United States