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Algorithms for representation theory of real reductive groups. (English) Zbl 1221.22017
Summary: 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 $$K(\mathbb C)$$ (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.

MSC:
 2.2e+51 Representations of Lie and linear algebraic groups over local fields 5e+99 Algebraic combinatorics
Software:
Atlas of Lie Groups
Full Text:
References:
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