Algorithms for Representation Theory of Real Reductive Groups

TL;DR

This paper presents an algorithm for computing irreducible admissible representations of real reductive groups with regular integral infinitesimal character, implemented in the Atlas project to advance representation theory computations.

Contribution

It introduces a novel algorithm for representation computation in real reductive groups, integrated into a computational framework for the first time.

Findings

Successful implementation of the algorithm in software.

Efficient computation of representations with regular integral infinitesimal character.

Enhanced capabilities for the Atlas of Lie Groups and Representations project.

Abstract

We give an algorithm for computing the irreducible admissible representations of a real reductive group with regular integral infinitesimal character. This algorithm has been implemented on a computer, as part of the Atlas of Lie Groups and Representations project.