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On Canonical Realizations of Bounded Symmetric Domains as Matrix-Spaces1)

Published online by Cambridge University Press:  22 January 2016

Mikio Ise
Mikio Ise*
Affiliation:
University of Tokyo
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It is the purpose of the present paper to give a natural method of realizing bounded symmetric domains as matrix-spaces. Our method yields, as special cases, the well-known bounded models of irreducible bounded symmetric domains of classical type (I)-(IV), as were already described in the original paper of E. Cartan [1] (see §3; we follow in this paper the classification table in [14], not in [1]). A direct application of this method will be to determine the canonical bounded models of the irreducible bounded symmetric domains of exceptional type; it will be published in another paper (see [6], [7] for the summary of the results).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 42 , March 1971 , pp. 115 - 133
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

Footnotes

1)

Part of the present work was done in 1964, when the author was staying at the Institute for Advanced Study, Princeton, under the sponsorship of the National Science Foundation.

References

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