Howe quotients of unitary characters and unitary lowest weight modules

DOI10.1090/S1088-4165-06-00279-2zbMath1133.22005OpenAlexW1509543870MaRDI QIDQ5445057

Huang Yean Loke

Publication date: 28 February 2008

Published in: Representation Theory of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1088-4165-06-00279-2

zbMATH Keywords

composition seriesunitary characterslocal theta liftsHowe quotientsunitary lowest weight modules

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Related Items

Degenerate principal series representations of \(\text{Sp}(p,q)\) ⋮ Hodge classes and the Jacquet–Langlands correspondence ⋮ Derived functor modules, dual pairs and \(\mathcal{U}(\mathfrak{g})^K\)-actions ⋮ Transfers of \(K\)-types on local theta lifts of characters and unitary lowest weight modules ⋮ The regularized Siegel-Weil formula (the second term identity) and the Rallis inner product formula ⋮ Dual pair correspondences for non-linear covers of orthogonal groups ⋮ On endoscopy and the refined Gross–Prasad conjecture for (SO₅, SO₄) ⋮ Degenerate principal series and local theta correspondence. III: The case of complex groups ⋮ Degenerate principal series representations for quaternionic unitary groups ⋮ Theta lifting of unitary lowest weight modules and their associated cycles ⋮ Invariants and -spectrums of local theta lifts ⋮ On the Siegel–Weil formula: The case of singular forms ⋮ On the regularized Siegel–Weil formula (the second term identity) and non-vanishing of theta lifts from orthogonal groups ⋮ Conservation relations for local theta correspondence

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Compositions of theta correspondences
• Theta lifting for unitary representations with nonzero cohomology
• Singular unitary representations of classical groups
• Degenerate principal series and invariant distributions
• The algebraic structure of the representation of semisimple Lie groups. I
• Diagrams for modules
• Representations of real reductive Lie groups
• Invariant distributions of classical groups
• On the Segal-Shale-Weil representations and harmonic polynomials
• Degenerate principal series and compact groups
• Young tableaux, Gelfand patterns, and branching rules for classical groups
• Degenerate principal series and local theta correspondence. II
• Discrete decomposability of the restriction of \(A_{{\mathfrak q}}(\lambda)\) with respect to reductive subgroups. III: Restriction of Harish-Chandra modules and associated varieties
• Analysis on the minimal representation of O(\(p,\) \(q\)). III: Ultrahyperbolic equations on \(\mathbb{R}^{p-1,q-1}\)
• Restrictions of quaternionic representations
• Theta lifting of unitary lowest weight modules and their associated cycles
• One-dimensional representations of \({U(p,q)}\) and the Howe correspondence
• On some degenerate principal series representations of \(U(n,n)\)
• Jordan algebras and generalized principal series representations
• Unitarizability of certain series of representations
• Degenerate principal series representations of \(\text{Sp}(p,q)\)
• On a problem of Klee concerning convex polytopes
• Theta lifting of holomorphic discrete series: The case of $ U(n, n) \times U(p, q) $
• Transcending Classical Invariant Theory
• On infinitesimal operators of irreducible representations of the Lorentz group of $n$-th order
• Remarks on Classical Invariant Theory
• On quaternionic discrete series representations, and their continuations.
• Differential operators and highest weight representations
• Singular unitary representations and discrete series for indefinite Stiefel manifolds 𝑈(𝑝,𝑞;𝐹)/𝑈(𝑝-𝑚,𝑞;𝐹)
• On certain distinguished unitary representations supported on null cones
• Unipotent representations attached to spherical nilpotent orbits
• Degenerate principal series and local theta correspondence
• THETA CORRESPONDENCE I — SEMISTABLE RANGE: CONSTRUCTION AND IRREDUCIBILITY
• Homogeneous functions on light cones: the infinitesimal structure of some degenerate principal series representations
• The duality correspondence of infinitesimal characters