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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 1625733
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Abstract: Let $D=G/K$ be a bounded symmetric domain and $K/L$ the Shilov boundary of $D$. Let $\mathcal{N}$ be the Shilov boundary of the Siegel domain realization of $G/K$. We consider the case when $D$ is the exceptional non-tube type domain of the type $(\mathfrak{e}_{6(-14)}, \mathfrak{so}(10)\times \mathfrak{so}(2))$. We prove that $(\mathcal{N}\rtimes L, L)$ 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: http://dx.doi.org/10.1090/S0002-9939-98-05051-5
PII: S 0002-9939(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