Generalized principal series representations and tube domains

DOI10.1215/S0012-7094-95-07815-6zbMath0841.22005MaRDI QIDQ1902014

Genkai Zhang, Bent Orsted

Publication date: 14 November 1995

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

intertwining operatorcharacterrepresentationLie algebrasoperatorprincipal series representationsuniversal covering grouphermitian formtube domaincomposition seriesShilov boundaryparabolic subgroupHarish-Chandra strongly orthogonal roots

Mathematics Subject Classification ID

Other representations of locally compact groups (22D12)

Related Items

Homogeneous vector bundles and intertwining operators for symmetric domains ⋮ Jordan algebras and generalized principal series representations ⋮ Laplace and Segal--Bargmann transforms on Hermitian symmetric spaces and orthogonal poly\-nomials. ⋮ Heisenberg parabolically induced representations of Hermitian Lie groups, part I: Intertwining operators and Weyl transform ⋮ Structure of the degenerate principal series on symmetric \(R\)-spaces and small representations ⋮ The Berezin form on symmetric $R$-spaces and reflection positivity ⋮ Fourier supports of K-finite Bessel integrals on classical tube domains ⋮ Generalized principal series representations of $SL(1+n,\mathbb {C})$ ⋮ Bessel operators on Jordan pairs and small representations of semisimple Lie groups ⋮ Degenerate principal series representations for quaternionic unitary groups ⋮ Tensor product of degenerate principal series and local theta correspondence ⋮ Degenerate principal series representations of \(\mathrm{SO}(p+1,p)\) ⋮ Unitary representations of Lie groups with reflection symmetry ⋮ Principal series of Hermitian Lie groups induced from Heisenberg parabolic subgroups ⋮ Covariant quantization: spectral analysis versus deformation theory ⋮ Intertwining operators for the generalized principal series on a symmetric 𝑅-space ⋮ Differential equations and recursion relations for Laguerre functions on symmetric cones

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