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