The action of an overalgebra on the Plancherel decomposition and shift operators in the imaginary direction
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Publication:4674565
DOI10.1070/IM2002v066n05ABEH000404zbMath1064.22005arXivmath/0202018OpenAlexW2057263213MaRDI QIDQ4674565
Publication date: 17 May 2005
Published in: Izvestiya: Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0202018
Semisimple Lie groups and their representations (22E46) Analysis on other specific Lie groups (43A80) Classical hypergeometric functions, ({}_2F_1) (33C05) Spectral synthesis on groups, semigroups, etc. (43A45)
Related Items (8)
Poisson and Fourier transforms for tensor products ⋮ Canonical representations and overgroups for hyperboloids ⋮ 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 ⋮ Canonical representations and overgroups for hyperboloids of one sheet and Lobachevsky spaces ⋮ Polynomial quantization and overalgebra ⋮ 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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