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

Koranyi, Adam and Misra, Gadadhar (2019) Homogeneous Hermitian holomorphic vector bundles and the Cowen-Douglas class over bounded symmetric domains. In: ADVANCES IN MATHEMATICS, 351 . pp. 1105-1138.

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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 Lie algebra on finite dimensional inner product spaces. The representations, and the induced bundles, have composition series with irreducible factors. Our first main result is the construction of an explicit differential operator intertwining the bundle with the direct sum of its factors. Next, we study Hilbert spaces of sections of these bundles. We use this to get, in particular, a full description and a similarity theorem for homogeneous n-tuples of operators in the Cowen-Douglas class of the Euclidean unit ball in C-n.

Item Type:	Journal Article
Publication:	ADVANCES IN MATHEMATICS
Publisher:	ACADEMIC PRESS INC ELSEVIER SCIENCE
Additional Information:	copyright for this article belongs to ACADEMIC PRESS INC ELSEVIER SCIENCE
Keywords:	Hermitizable homogeneous; holomorphic vector bundles; Holomorphic induction; Cowen-Douglas class
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	07 Aug 2019 05:47
Last Modified:	07 Aug 2019 05:47
URI:	http://eprints.iisc.ac.in/id/eprint/63361

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