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2009•Kyushu Journal of MathematicsOpen access

THE REPRESENTATIVE DOMAIN OF A HOMOGENEOUS BOUNDED DOMAIN

Hideyuki Ishi, Chifune Kai

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Abstract

The representative domain gives a nice realization for a homogeneous bounded domain, which is a generalization of the Harish-Chandra realization for a symmetric bounded domain. We show that the representative domain coincides with the image of the Cayley transform introduced by Penney and Nomura. As an application, we see that a homogeneous bounded domain is symmetric if and only if its representative domain is convex.

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The representative domain gives a nice realization for a homogeneous bounded domain, which is a generalization of the Harish-Chandra realization for a symmetric bounded domain. We show that the representative domain coincides with the image of the Cayley transform introduced by Penney and Nomura. As an application, we see that a homogeneous bounded domain is symmetric if and only if its representative domain is convex.

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Available abstract

The representative domain gives a nice realization for a homogeneous bounded domain, which is a generalization of the Harish-Chandra realization for a symmetric bounded domain. We show that the representative domain coincides with the image of the Cayley transform introduced by Penney and Nomura. As an application, we see that a homogeneous bounded domain is symmetric if and only if its representative domain is convex.

Key concepts: Bounded function, Mathematics, Domain (mathematical analysis), Homogeneous, Realization (probability), Effective domain, Regular polygon, Pure mathematics

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