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Equivariant holomorphic maps into the Siegel disc and the metaplectic representation

Part of: Lie groups Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

Jean-Louis Clerc
Jean-Louis Clerc
Affiliation:
Institut Elie Cartan Université Henri Poincaré Nancy 1B.P. 239 54506 Vandoeuvre-lès-Nancy CedexFrance e-mail: clerc@iecn.u-nancy.fr
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Abstract

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We restrict the metaplectic representation to subgroups G of the symplectic group associated to equivariant holomorphic maps into the Siegel disc. We describe the invariant subspaces of the decomposition, and reduce the problem to the decomposition of a space of ‘harmonic’ polynomials under the action of the maximal compact subgroup of G.

MSC classification

Secondary: 22E46: Semisimple Lie groups and their representations 43A85: Analysis on homogeneous spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 62 , Issue 2 , April 1997 , pp. 160 - 174
Copyright
Copyright © Australian Mathematical Society 1997

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