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.
