The Capelli identity, tube domains, and the generalized Laplace transform

DOI10.1016/0001-8708(91)90062-CzbMath0748.22008MaRDI QIDQ1814130

Siddhartha Sahi, Bertram Kostant

Publication date: 25 June 1992

Published in: Advances in Mathematics (Search for Journal in Brave)

zbMATH Keywords

symmetric spacedifferential operatorCapelli identityJordan algebrareductive Lie algebradifferential identitiespositive definite Hermitian matrices

Mathematics Subject Classification ID

Lie algebras of vector fields and related (super) algebras (17B66) Harmonic analysis on homogeneous spaces (43A85) Lie algebras of Lie groups (22E60) Finite-dimensional structures of Jordan algebras (17C55)

Related Items

On a q-analog of a Sahi result, Z-graduations de type parabolique et polynomes harmoniques, The asymptotics of spherical functions and the central limit theorem on symmetric cones, The Capelli problem for \(\mathfrak{gl}(m|n)\) and the spectrum of invariant differential operators, Jordan algebras and generalized principal series representations, Generalized principal series representations and tube domains, The Berezin transform and invariant differential operators, Bihomogeneous symmetric functions, Quantum immanants and higher Capelli identities, Algebraic/combinatorial proofs of Cayley-type identities for derivatives of determinants and Pfaffians, Quantum immanants, double Young–Capelli bitableaux and Schur shifted symmetric functions, Capelli-Deruyts bitableaux and the classical Capelli generators of the center of the enveloping algebra U( gl ( n )), Heisenberg parabolically induced representations of Hermitian Lie groups, part I: Intertwining operators and Weyl transform, Explicit Hilbert spaces for certain unipotent representations, Unnamed Item, Unnamed Item, The Capelli eigenvalue problem for Lie superalgebras, Schur 𝑄-functions and the Capelli eigenvalue problem for the Lie superalgebra \ger𝑞(𝑛), Explicit Newton's formula for \({\mathfrak gl}_n\), The Capelli identity for Grassmann manifolds, A nonsymmetric version of Okounkov's BC-type interpolation Macdonald polynomials, Covariant quantization: spectral analysis versus deformation theory, Young–Capelli bitableaux, Capelli immanants in U(gl(n)) and the Okounkov quantum immanants, The Harish-Chandra homomorphism for a quantized classical Hermitian symmetric pair, Geometric quantization of real minimal nilpotent orbits, On Turnbull identity for skew-symmetric matrices, Capelli operators for spherical superharmonics and the Dougall-Ramanujan identity, The Capelli identity, the double commutant theorem, and multiplicity-free actions, Jordan algebras and Capelli identities, A theory of noncommutative determinants and characteristic functions of graphs

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