Pure and Applied Mathematics Quarterly

Volume 17 (2021)

Number 2

Special Issue: In Honor of David Mumford

Guest Editors: Ching-Li Chai, Amnon Neeman

Cartan–Iwahori–Matsumoto decompositions for reductive groups

Pages: 593 – 604

DOI: https://dx.doi.org/10.4310/PAMQ.2021.v17.n2.a1


Jarod Alper (Department of Mathematics, University of Washington, Seattle, Wa., U.S.A.)

Jochen Heinloth (Fakultät für Mathematik, Universität Duisburg-Essen, Essen, Germany)

Daniel Halpern-Leistner (Department of Mathematics, Cornell University, Ithaca, New York, U.S.A.)


We provide a short and self-contained argument for the existence of Cartan–Iwahori–Matsumoto decompositions for reductive groups.


reductive groups, geometric invariant theory

2010 Mathematics Subject Classification

Primary 14L24, 14L35. Secondary 13A50.

The first-named author was partially supported by NSF grant DMS-1801976.

The second-named author was partially supported by NSF grant DMS-1762669.

The third-named author was partially supported by Sonderforschungsbereich/Transregio 45 of the DFG.

Received 1 March 2019

Accepted 7 August 2019

Published 12 May 2021