Vol. 302, No. 1, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 310: 1
Vol. 309: 1  2
Vol. 308: 1  2
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
The compact picture of symmetry-breaking operators for rank-one orthogonal and unitary groups

Jan Frahm and Bent Ørsted

Vol. 302 (2019), No. 1, 23–76

We present a method to calculate intertwining operators between the underlying Harish-Chandra modules of degenerate principal series representations of a reductive Lie group G and a reductive subgroup G , and between their composition factors. Our method describes the restriction of these operators to the K-isotypic components, K G a maximal compact subgroup, and reduces the representation-theoretic problem to an infinite system of scalar equations of a combinatorial nature. For rank-one orthogonal and unitary groups and spherical principal series representations we calculate these relations explicitly and use them to classify intertwining operators. We further show that in these cases automatic continuity holds; i.e., every intertwiner between the Harish-Chandra modules extends to an intertwiner between the Casselman–Wallach completions, verifying a conjecture by Kobayashi. Altogether, this establishes the compact picture of the recently studied symmetry-breaking operators for orthogonal groups by Kobayashi and Speh, gives new proofs of their main results, and extends them to unitary groups.

PDF Access Denied

However, your active subscription may be available on Project Euclid at

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

symmetry-breaking operators, intertwining operators, Harish-Chandra modules, principal series, spectrum-generating operator
Mathematical Subject Classification 2010
Primary: 22E46
Secondary: 05E10, 17B15
Received: 14 February 2017
Accepted: 29 October 2018
Published: 5 November 2019
Jan Frahm
Department of Mathematics
Aarhus University
Bent Ørsted
Department of Mathematics
Aarhus University