Bessel functions and representation theory. II: Holomorphic discrete series and metaplectic representations

DOI10.1016/0022-1236(77)90030-1zbMath0361.22007OpenAlexW1972384070MaRDI QIDQ1239393

Ray A. Kunze, Kenneth I. Gross

Publication date: 1977

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

Full work available at URL: https://doi.org/10.1016/0022-1236(77)90030-1

Mathematics Subject Classification ID

Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45)

Related Items

Weighted Laplace transforms and Bessel functions on Hermitian symmetric spaces, Bessel functions associated with representations of formally real Jordan algebras, Hermitian Lie Algebras and Metaplectic Representations. I, A quantization of the Cartan domain BD I \((q=2)\) and operators on the light cone, Restrictions and expansions of holomorphic representations, Determinantal ideals and the canonical commutation relations: classically or quantized, \((\mathrm{GL}_n,\mathrm{GL}_m)\)-duality and symmetric plethysm, Operator-valued Bessel functions on Schrödinger-Fock spaces and Siegel domains of type II, Invariant distributions of classical groups, Operator-valued Bessel functions, holomorphic discrete series, and harmonic representations of \(U(p,q)\), Discrete spectrum of the reductive dual pair \((\mathrm{O}(p,q),\mathrm{Sp}(2m))\), On the Segal-Shale-Weil representations and harmonic polynomials, Transcending Classical Invariant Theory, Generalized Bessel functions and the representation theory of U(2) σ C2×2, Tensor products, reproducing kernels, and power series, A description of a space of holomorphic discrete series by means of the Fourier transform on the Šilov boundary, Bessel systems for Jordan algebras of rank 2 and 3, Remarks on Classical Invariant Theory

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