The harmonic representation of U(p,q) and its connection with the generalized unit disk

DOI10.2140/pjm.1987.129.33zbMath0577.43003OpenAlexW2081882566MaRDI QIDQ1066038

Mark G. Davidson

Publication date: 1987

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.1987.129.33

zbMATH Keywords

intertwining operatorHilbert spaceFock spacetensor productoscillator representationSegal-Shale-Weil representationvector-valued holomorphic functionsU(p,q)generalized unit diskharmonic representationmultiplier representation

Mathematics Subject Classification ID

Homomorphisms and multipliers of function spaces on groups, semigroups, etc. (43A22) Analysis on real and complex Lie groups (22E30) Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) (43A65) Hilbert spaces of continuous, differentiable or analytic functions (46E20)

Related Items (4)

An \(L^ 2\)-cohomology construction of negative spin mass zero equations for U(p,q) ⋮ Gradient-type differential operators and unitary highest weight representations of SU(p,q) ⋮ A note on the harmonic representation of \(\mathrm{SU}(p,q)\) ⋮ Operator-valued Bessel functions, holomorphic discrete series, and harmonic representations of \(U(p,q)\)

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