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Determinant Type Differential Operators on Homogeneous Siegel Domains

✍ Scribed by Hideyuki Ishi

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
186 KB
Volume
183
Category
Article
ISSN
0022-1236

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✦ Synopsis

We study the differential operators whose symbols are determinant type polynomials associated to homogeneous cones in connection with unitary representations of the split solvable Lie group acting simply transitively on a Siegel domain.

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Let D be a bounded homogeneous domain in C n . (Note that D is not assumed to be Hermitian-symmetric.) In this work we are interested in studying various classes of ``harmonic'' functions on D and the possibility of representing them as ``Poisson integrals'' over the Bergman-Shilov boundary. One suc