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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Vogan duality for nonlinear type B
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by Scott Crofts PDF
Represent. Theory 15 (2011), 258-306 Request permission

Abstract:

Let $\mathbb {G}=\mathrm {Spin}[4n+1]$ be the connected, simply connected complex Lie group of type $B_{2n}$ and let $G=\mathrm {Spin}(p,q)$ $(p+q=4n+1)$ denote a (connected) real form. If $q \notin \left \{0,1\right \}$, $G$ has a nontrivial fundamental group and we denote the corresponding nonalgebraic double cover by $\tilde {G}=\widetilde {\mathrm {Spin}}(p,q)$. The main purpose of this paper is to describe a symmetry in the set of genuine parameters for the various $\tilde {G}$ at certain half-integral infinitesimal characters. This symmetry is used to establish a duality of the corresponding generalized Hecke modules and ultimately results in a character multiplicity duality for the genuine characters of $\tilde {G}$.
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Additional Information
  • Scott Crofts
  • Affiliation: Department of Mathematics, University of California, Santa Cruz, California 95064
  • Received by editor(s): August 13, 2009
  • Received by editor(s) in revised form: August 5, 2010
  • Published electronically: March 24, 2011
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 15 (2011), 258-306
  • MSC (2010): Primary 20G05
  • DOI: https://doi.org/10.1090/S1088-4165-2011-00398-8
  • MathSciNet review: 2788895