Algorithms for representation theory of real reductive groups

Abstract

AbstractThe admissible representations of a real reductive groupGare known by work of Langlands, Knapp, Zuckerman and Vogan. This paper describes an effective algorithm for computing the irreducible representations ofGwith regular integral infinitesimal character. The algorithm also describes structure theory ofG, including the orbits ofK(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.