CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

Stable Discrete Series Characters at Singular Elements

  Published:2009-12-01
 Printed: Dec 2009
  • Steven Spallone
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

Write $\Theta^E$ for the stable discrete series character associated with an irreducible finite-dimensional representation $E$ of a connected real reductive group $G$. Let $M$ be the centralizer of the split component of a maximal torus $T$, and denote by $\Phi_M(\gm,\Theta^E)$ Arthur's extension of $ |D_M^G(\gm)|^{\lfrac 12} \Theta^E(\gm)$ to $T(\R)$. In this paper we give a simple explicit expression for $\Phi_M(\gm,\Theta^E)$ when $\gm$ is elliptic in $G$. We do not assume $\gm$ is regular.
MSC Classifications: 22E47 show english descriptions Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) [See also 17B10] 22E47 - Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) [See also 17B10]
 

© Canadian Mathematical Society, 2014 : https://cms.math.ca/