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Algorithms for representation theory of real reductive groups

Part of: Algebraic combinatorics Lie groups

Published online by Cambridge University Press:  06 January 2009

Jeffrey Adams  and
Fokko du Cloux
Jeffrey Adams
Affiliation:
Department of Mathematics, Mathematics Building, University of Maryland, College Park, MD 20742-4015, USA (jda@math.umd.edu)
Fokko du Cloux
Affiliation:
Department of Mathematics, Mathematics Building, University of Maryland, College Park, MD 20742-4015, USA (jda@math.umd.edu)
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Abstract

The admissible representations of a real reductive group G are known by work of Langlands, Knapp, Zuckerman and Vogan. This paper describes an effective algorithm for computing the irreducible representations of G with regular integral infinitesimal character. The algorithm also describes structure theory of G, including the orbits of K(ℂ) (a complexified maximal compact subgroup) on the flag variety. This algorithm has been implemented on a computer by the second author, as part of the ‘Atlas of Lie Groups and Representations’ project.

Keywords

Lie groupsrepresentation theoryreal reductive groupsalgorithmsadmissible representationscomputational representation theory

MSC classification

Secondary: 22E50: Representations of Lie and linear algebraic groups over local fields 05E99: None of the above, but in this section
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 8 , Issue 2 , April 2009 , pp. 209 - 259
Copyright
Copyright © Cambridge University Press 2009

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