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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:
22E50 Representations of Lie and linear algebraic groups over local fields
05E99 Algebraic combinatorics
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