Eigenfunction expansion associated with the Casimir operator on the quantum group \(SU_ q(1,1)\)

DOI10.1215/S0012-7094-95-08019-3zbMath0846.17014OpenAlexW2054892191MaRDI QIDQ1913366

Tomoyuki Kakehi

Publication date: 14 May 1996

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-95-08019-3

zbMATH Keywords

Plancherel formulabasic hypergeometric functionseigenfunction expansionCasimir operatorquantum group \(\text{SU}_ q (1,1)\)

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Analysis on other specific Lie groups (43A80) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items (3)

Transmutation kernels for the little \(q\)-Jacobi function transform. ⋮ One-parameter orthogonality relations for basic hypergeometric series ⋮ The vector-valued big \(q\)-Jacobi transform

Cites Work

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• Spherical functions on the quantum group \(\text{SU}(1,1)\) and the \(q\)-analogue of the Mehler-Fock formula
• Quantum deformation of Lorentz group
• Unitary representations of the quantum group \(\text{SU}_q(1,1)\): structure of the dual space of \({\mathcal U}_q(\mathfrak{sl}(2))\)
• Unitary representations of the quantum group \(\text{SU}_q(1,1)\). II: Matrix elements of unitary representations and the basic hypergeometric functions
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Compact matrix pseudogroups
• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• Representations of the quantum group \(SU_ q(2)\) and the little q-Jacobi polynomials
• Quantum group \(\text{SU}(1,1)\rtimes\mathbb Z_ 2\) and ``super-tensor products
• Spectral analysis for the Casimir operator on the quantum group \(SU_ q(1,1)\)
• Irreducible unitary representations of the Lorentz group
• Connection problem in holonomicq-difference system associated with a Jackson integral of Jordan-Pochhammer type

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