Homogeneous Hermitian holomorphic vector bundles and the Cowen-Douglas class over bounded symmetric domains

Koranyi, Adam and Misra, Gadadhar (2016) Homogeneous Hermitian holomorphic vector bundles and the Cowen-Douglas class over bounded symmetric domains. In: COMPTES RENDUS MATHEMATIQUE, 354 (3, 201). pp. 291-295.

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Abstract

It is known that all the vector bundles of the title can be obtained by holomorphic induction from representations of a certain parabolic group on finite-dimensional inner product spaces. The representations, and the induced bundles, have composition series with irreducible factors. We write down an equivariant constant coefficient differential operator that intertwines the bundle with the direct sum of its irreducible factors. As an application, we show that in the case of the closed unit ball in C-n all homogeneous n-tuples of Cowen-Douglas operators are similar to direct sums of certain basic n-tuples. (c) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Item Type:	Journal Article
Publication:	COMPTES RENDUS MATHEMATIQUE
Publisher:	ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER
Additional Information:	Copy right for this article belongs to the ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER, 23 RUE LINOIS, 75724 PARIS, FRANCE
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	12 May 2016 07:39
Last Modified:	12 May 2016 07:39
URI:	http://eprints.iisc.ac.in/id/eprint/53793

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