On the distinction of Iwahori-spherical representations

2020/12/02 by Broussous, Paul
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2012.01200

Abstract

Let E/F be a quadratic unramified extension of non-archimedean local fields and \mathbb H a simply connected semisimple algebraic group defined and split over F. We establish general results (multiplicities, test vectors) on \HH (F)-distinguished Iwahori-spherical representations of \HH (E). For discrete series Iwahori-spherical representations of \HH (E), we prove a numerical criterion of \HH (F)-distinction. As an application, we classify the \HH (F)-distinguished discrete series representations of \HH (E) corresponding to degree 1 characters of the Iwahori-Hecke algebra.

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