Degenerate principal series representations of \(GL_n(\mathbb{C})\) and \(GL_n(\mathbb{R})\)

DOI10.1006/jfan.1999.3427zbMath0941.22016OpenAlexW2085821334MaRDI QIDQ1304673

Soo Teck Lee, Roger E. Howe

Publication date: 3 August 2000

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1999.3427

zbMATH Keywords

composition seriesdegenerate principal series representationshighest weight vectorsStein complementary series\(K\)-types

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46)

Related Items (26)

Nearly holomorphic automorphic forms on \(\mathrm{SP}_{2n}\) with sufficiently regular infinitesimal characters and applications ⋮ Symmetry breaking operators for line bundles over real projective spaces ⋮ Degenerate principal series for even-orthogonal groups ⋮ Real double flag varieties for the symplectic group ⋮ The Heisenberg ultrahyperbolic equation: \(K\)-finite and polynomial solutions ⋮ Non-Siegel Eisenstein series for symplectic groups ⋮ Invariant functionals on Speh representations ⋮ Quasianalyticity, uncertainty, and integral transforms on higher Grassmannians ⋮ Irreducible representations of \(\mathrm{GL}_n (\mathbb{C})\) of minimal Gelfand-Kirillov dimension ⋮ Geometric analysis on small unitary representations of \(\text{GL}(N, \mathbb R)\) ⋮ Structure of the degenerate principal series on symmetric \(R\)-spaces and small representations ⋮ On extendability by continuity of valuations on convex polytopes ⋮ Degenerate Eisenstein series for \(\operatorname{Sp}(4)\) ⋮ The regularized Siegel-Weil formula (the second term identity) and the Rallis inner product formula ⋮ Covariants of Sp\(_{n}(\mathbb C)\) and degenerate principal series of GL\(_{n}(\mathbb H)\) ⋮ Lie algebras of vector fields on smooth affine varieties ⋮ Degenerate principal series and local theta correspondence. III: The case of complex groups ⋮ On GL _n (ℝ)‐invariant classes of convex bodies ⋮ On the Siegel–Weil formula: The case of singular forms ⋮ Degenerate principal series representations of \(\mathrm{SO}(p+1,p)\) ⋮ Range characterization of the cosine transform on higher Grassmannians ⋮ Homogeneous distributions on finite dimensional vector spaces ⋮ Covariant quantization: spectral analysis versus deformation theory ⋮ On P. McMullen's conjecture on translation invariant valuations ⋮ Berezin kernels and maximal degenerate representations associated with Riemannian symmetric spaces of Hermitian type ⋮ Branching laws for small unitary representations of GL(n, ℂ)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Capelli identity, the double commutant theorem, and multiplicity-free actions
• The unitary dual of \(\mathrm{GL}(n)\) over an archimedean field
• Group representations arising from Lorentz conformal geometry
• Degenerate principal series and compact groups
• On some degenerate principal series representations of \(U(n,n)\)
• Some simple examples in the representation theory of semisimple Lie groups
• On certain rings of highest weight vectors
• Jordan algebras and generalized principal series representations
• Spectrum generating operators and intertwining operators for representations induced from a maximal parabolic subgroup
• Analysis in matrix spaces and some new representations of \(SL(N,\mathbb{C})\)
• Infinitesimal operators and structure of the most degenerate representations of the groups Sp( p+q) and Sp( p, q) in an Sp( p)×Sp(q) basis
• Homogeneous functions on light cones: the infinitesimal structure of some degenerate principal series representations
• Jordan algebras and degenerate principal series.

This page was built for publication: Degenerate principal series representations of \(GL_n(\mathbb{C})\) and \(GL_n(\mathbb{R})\)