Operators, Fuchsian groups, and automorphic bundles

Wilkins, David R.

doi:10.1007/bf01459251

Cited by 5 publications

(3 citation statements)

References 6 publications

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“…The group G is isomorphic to the quotient group H/H 0 . Question whether the group G admits a unitary representation was discussed in [5,9,18,21]. Paper [5] contains a list of open problems related to this topic, as well as further references.…”

Section: Automorphic Invariant Isometric Operators 597mentioning

confidence: 99%

“…Such operators we call automorphic invariant. Another term that is used in literature for contractive operators that are unitarily equivalent to their Möbius transformations is "homogeneous" [5,9,18,21]. The term "automorphic invariant" was borrowed from [11] where two theorems about J-unitary automorphic invariant operator colligations were formulated without proofs.…”

Section: Introductionmentioning

confidence: 99%

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Automorphic Invariant Isometric Operators

Bekker

2008

Complex Anal. Oper. Theory

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We consider isometric operators with finite defect numbers that are unitarily equivalent to their Möbius transformations. A functional characterization of such isometries is given in terms of their characteristic operatorfunctions. We show that any such isometry admits a contractive extension that is also unitarily equivalent to its Möbius transformation and a unitary extension in a larger space that has the same property. Examples of automorphic invariant operators are considered. Mathematics Subject Classification (2000). Primary 47B99; Secondary 30D55.

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Section: Automorphic Invariant Isometric Operators 597mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Automorphic Invariant Isometric Operators

Bekker

2008

Complex Anal. Oper. Theory

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“…Homogeneous operators in B r (Ω) with respect to the automorphism group of an irreducible bounded symmetric domain Ω have been studied in [8,11,15].…”

Section: Introductionmentioning

confidence: 99%

Homogeneous Hermitian Holomorphic Vector Bundles And Operators In The Cowen-Douglas Class Over The Poly-disc

Deb¹,

Hazra²

2020

Preprint

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In this article, we obtain two sets of results. The first set of complete results are exclusively for the case of the bi-disc while the second set of results describe in part, which of these carry over to the general case of the poly-disc:A classification of irreducible hermitian holomorphic vector bundles over D 2 , homogeneous with respect to Möb × Möb, is obtained assuming that the associated representations are multiplicity-free. Among these the ones that give rise to an operator in the Cowen-Douglas class of D 2 of rank 1, 2 or 3 is determined. Any hermitian holomorphic vector bundle of rank 2 over D n , homogeneous with respect to the n-fold product of the group Möb is shown to be a tensor product of n − 1 hermitian holomorphic line bundles, each of which is homogeneous with respect to Möb and a hermitian holomorphic vector bundle of rank 2, homogeneous with respect to Möb. The classification of irreducible homogeneous hermitian holomorphic vector bundles over D 2 of rank 3 (as well as the corresponding Cowen-Douglas class of operators) is extended to the case of D n , n > 2. It is shown that there is no irreducible n -tuple of operators in the Cowen-Douglas class B2(D n ) that is homogeneous with respect to Aut(D n ), n > 1. Also, pairs of operators in B3(D 2 ) homogeneous with respect to Aut(D 2 ) are produced, while it is shown that no ntuple of operators in B3(D n ) is homogeneous with respect to Aut(D n ), n > 2.

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Homogeneous operators and projective representations of the Möbius group: A survey

Bagchi

Misra

2001

Proc. Math. Sci.

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Operators, Fuchsian groups, and automorphic bundles

Cited by 5 publications

References 6 publications

Automorphic Invariant Isometric Operators

Automorphic Invariant Isometric Operators

Homogeneous Hermitian Holomorphic Vector Bundles And Operators In The Cowen-Douglas Class Over The Poly-disc

Homogeneous operators and projective representations of the Möbius group: A survey

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