Some regular symmetric pairs

Authors:
Avraham Aizenbud and Dmitry Gourevitch

Journal:
Trans. Amer. Math. Soc. **362** (2010), 3757-3777

MSC (2010):
Primary 20G05, 20G25, 22E45

DOI:
https://doi.org/10.1090/S0002-9947-10-05008-7

Published electronically:
February 12, 2010

MathSciNet review:
2601608

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Abstract | References | Similar Articles | Additional Information

Abstract: In an earlier paper we explored the question what symmetric pairs are Gelfand pairs. We introduced the notion of regular symmetric pair and conjectured that all symmetric pairs are regular. This conjecture would imply that many symmetric pairs are Gelfand pairs, including all connected symmetric pairs over .

In this paper we show that the pairs , are regular, where and are quadratic or Hermitian spaces over an arbitrary local field of characteristic zero. We deduce from this that the pairs and are Gelfand pairs.

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Additional Information

**Avraham Aizenbud**

Affiliation:
Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, POB 26, Rehovot 76100, Israel

Email:
aizenr@yahoo.com

**Dmitry Gourevitch**

Affiliation:
Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, POB 26, Rehovot 76100, Israel

Address at time of publication:
School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540

Email:
guredim@yahoo.com

DOI:
https://doi.org/10.1090/S0002-9947-10-05008-7

Keywords:
Uniqueness,
multiplicity one,
Gelfand pair,
symmetric pair,
unitary group,
orthogonal group

Received by editor(s):
September 11, 2008

Published electronically:
February 12, 2010

Additional Notes:
Both authors were partially supported by a BSF grant, a GIF grant, and an ISF Center of excellency grant. The first author was also supported by ISF grant No. 583/09 and the second author by NSF grant DMS-0635607. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.