Algebras of invariant functions

on the Shilov boundaries of Siegel domains

Authors:
Anthony H. Dooley and Genkai Zhang

Journal:
Proc. Amer. Math. Soc. **126** (1998), 3693-3699

MSC (1991):
Primary 22E46, 32M15

DOI:
https://doi.org/10.1090/S0002-9939-98-05051-5

MathSciNet review:
1625733

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a bounded symmetric domain and the Shilov boundary of . Let be the Shilov boundary of the Siegel domain realization of . We consider the case when is the exceptional non-tube type domain of the type . We prove that is not a Gelfand pair and thus resolve an open question of G. Carcano.

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Additional Information

**Anthony H. Dooley**

Affiliation:
School of Mathematics, University of New South Wales, Sydney 2052, Australia

Email:
a.dooley@unsw.edu.au

**Genkai Zhang**

Affiliation:
School of Mathematics, University of New South Wales, Sydney 2052, Australia

Address at time of publication:
Department of Mathematics, University of Karlstad, S-65188 Karlstad, Sweden

Email:
genkai.zhang@hks.se

DOI:
https://doi.org/10.1090/S0002-9939-98-05051-5

Keywords:
Bounded symmetric domain,
exceptional Lie algebra,
Gelfand pair,
spin representation,
Jordan pair

Received by editor(s):
March 25, 1995

Additional Notes:
This research was sponsored by the Australian Research Council.

Communicated by:
J. Marshall Ash

Article copyright:
© Copyright 1998
American Mathematical Society