Canonical representations on Lobachevsky spaces: An interaction with an overalgebra

zbMath1134.43002MaRDI QIDQ2464062

Vladimir F. Molchanov

Publication date: 10 December 2007

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

zbMATH Keywords

Lie groupsLie algebrasSymmetric spacesBerezin formBoundary representationsCanonical representationsHyperboloidsLobachevsky spacesPoisson and Fourier transforms

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85) Semisimple Lie groups and their representations (22E46)

Related Items (5)

Poisson and Fourier transforms for tensor products ⋮ The Fourier transform on the group \(\mathrm{GL}_2(\mathbb{R})\) and the action of the overalgebra \(\mathfrak{gl}_4\) ⋮ Operational calculus for the Fourier transform on the group \(\mathrm{GL}(2,\mathbb{R})\) and the problem about the action of an overalgebra in the Plancherel decomposition ⋮ Restriction of representations of \(\mathrm{GL}(n + 1, \mathbb{C})\) to \(\mathrm{GL}(n, \mathbb{C})\) and action of the Lie overalgebra ⋮ Fourier transform on the Lobachevsky plane and operational calculus

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