Models ofQ-Algebra Representations: The Group of Plane Motions

DOI10.1137/S0036141092224613zbMath0805.33020OpenAlexW2082322092MaRDI QIDQ4292647

Willard jun. Miller, Ernest G. Kalnins, Sanchita Mukherjee

Publication date: 31 January 1995

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0036141092224613

zbMATH Keywords

\(q\)-algebrasquantum groupsClebsch-Gordan coefficients\(q\)-Bessel functions

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items (16)

\(3nj\)-symbols and identities for \(q\)-Bessel functions ⋮ The quantum group of plane motions and the Hahn-Exton \(q\)-Bessel function ⋮ Quantum algebra approach to \(q\)-Gegenbauer polynomials ⋮ A \(q^ 2\)-analogue operator for \(q^ 2\)-analogue Fourier analysis ⋮ \(q\)-gamma and \(q\)-beta functions in quantum algebra representation theory ⋮ A note on tensor products of \(q\)-algebra representations and orthogonal polynomials ⋮ Yet another basic analogue of Graf's addition formula ⋮ Quantum algebra \(\varepsilon_q(2)\) and 2D \(q\)-Bessel functions ⋮ Generalized \(q\)-Bessel function and its properties ⋮ On \(q\)-special matrix functions using quantum algebraic techniques ⋮ On irreducible \(p,q\)-representations of gl(2). ⋮ \(q\)-Tricomi functions and quantum algebra representations ⋮ On models of certain \(p,q\)-algebra representations: the quantum Euclidean algebra \(\mathcal E _{p,q}(2)\) ⋮ Unnamed Item ⋮ On models of certain p,q-algebra representations: The p,q-oscillator algebra ⋮ Toeplitz matrices and classical and \(q\)-Bessel functions

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