The unitary representations parametrized by the Wallach set for a homogeneous bounded domain

Ishi, Hideyuki

doi:10.1515/apam-2013-0206

Cited by 3 publications

(2 citation statements)

References 9 publications

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“…The mapping σ is called the Bergman mapping (see [12] and [22]), which was shown in [13] to be equal to 1 2 times the Cayley transform of the Siegel domain D, introduced by Penney [18]. The following theorem is fundamental (see [13], [17], [18] and [22]).…”

Section: First Proof Of Theorem 11mentioning

confidence: 99%

Korányi’s Lemma for Homogeneous Siegel Domains of Type Ii. Applications and Extended Results

Békollè¹,

Ishi²,

Nana³

2014

Bull. Aust. Math. Soc.

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We show that the modulus of the Bergman kernel $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}B(z, \zeta )$ of a general homogeneous Siegel domain of type II is ‘almost constant’ uniformly with respect to $z$ when $\zeta $ varies inside a Bergman ball. The control is expressed in terms of the Bergman distance. This result was proved by A. Korányi for symmetric Siegel domains of type II. Subsequently, R. R. Coifman and R. Rochberg used it to establish an atomic decomposition theorem and an interpolation theorem by functions in Bergman spaces $A^p$ on these domains. The atomic decomposition theorem and the interpolation theorem are extended here to the general homogeneous case using the same tools. We further extend the range of exponents $p$ via functional analysis using recent estimates.

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Section: First Proof Of Theorem 11mentioning

confidence: 99%

Korányi’s Lemma for Homogeneous Siegel Domains of Type Ii. Applications and Extended Results

Békollè¹,

Ishi²,

Nana³

2014

Bull. Aust. Math. Soc.

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“…Theorem 1.6 (Ishi, [16]). Unitarizations of T J −γ and T J −γ ′ are equivalent as unitary representations of Aut hol (D) o if and only if γ = γ ′ .…”

Section: Introductionmentioning

confidence: 99%

Holomorphic multiplier representations for bounded homogeneous domains

Arashi

2019

Preprint

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In this paper, we study the unitarizations in the spaces of holomorphic sections of equivariant holomorphic line bundles over a bounded homogeneous domain under the action of a connected algebraic group acting transitively on the domain. We give a complete classification of unitary representations arising from such unitarizations. As an application, we classify all such unitary representations for a specific five-dimensional non-symmetric bounded homogeneous domain.

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Homogeneous Kähler Manifolds

Loi

Zedda

2018

Kähler Immersions of Kähler Manifolds Into Complex Space Forms

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The unitary representations parametrized by the Wallach set for a homogeneous bounded domain

Cited by 3 publications

References 9 publications

Korányi’s Lemma for Homogeneous Siegel Domains of Type Ii. Applications and Extended Results

Korányi’s Lemma for Homogeneous Siegel Domains of Type Ii. Applications and Extended Results

Holomorphic multiplier representations for bounded homogeneous domains

Homogeneous Kähler Manifolds

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