Pure and Applied Mathematics Quarterly

Volume 17 (2021)

Number 4

Special Issue: In Memory of Prof. Bertram Kostant

Guest Editors: Shrawan Kumar, Lizhen Ji, and Kefeng Liu

Associated varieties for real reductive groups

Pages: 1191 – 1267

DOI:  https://dx.doi.org/10.4310/PAMQ.2021.v17.n4.a2

Authors

Jeffrey Adams (Department of Mathematics, University of Maryland, College Park, Md., U.S.A.)

David A. Vogan, Jr. (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)

Abstract

We give an algorithm to compute the associated variety of a Harish–Chandra module for a real reductive group $G(\mathbb{R})$. The algorithm is implemented in the atlas software package.

Keywords

reductive group, representation, orbit method

2010 Mathematics Subject Classification

22E45

In fond memory of our teacher and friend, Bert Kostant.

J. A. is supported in part by NSF grant DMS-1317523.

Received 17 June 2019

Accepted 22 March 2021

Published 22 December 2021