A family of quantum projective spaces and related $q$-hypergeometric orthogonal polynomials

DOI10.1090/S0002-9947-98-01971-0zbMath0906.33011arXivq-alg/9605017OpenAlexW1825148609MaRDI QIDQ4211101

Masatoshi Noumi, Mathijs S. Dijkhuizen

Publication date: 10 September 1998

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-alg/9605017

zbMATH Keywords

Casimir operatorAskey-Wilson polynomialsradial partquantum projective spacezonal spherical functionsecond-order \(q\)-difference operatorquantum unitary groupbig and little \(q\)-Jacobi polynomialstwo-sided coideal

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items

Pseudo-symmetric pairs for Kac-Moody algebras, Quantum zonal spherical functions and Macdonald polynomials, Pairings and actions for dynamical quantum groups, COIDEAL SUBALGEBRAS IN QUANTUM AFFINE ALGEBRAS, Invariants and orthogonal \(q\)-polynomials associated with \(\mathbb {C}_{q}( \operatorname{osp}(1,2))\), Branching rules for finite-dimensional \(\mathcal {U}_{q}(\mathfrak {su}(3))\)-representations with respect to a right coideal subalgebra, Universal K-matrices for quantum Kac-Moody algebras, Coideal algebras from twisted Manin triples, Nonstandard quantum complex projective line, Some limit transitions between BC type orthogonal polynomials interpreted on quantum complex Grassmannians, The dynamical \(U(n)\) quantum group, Right coideal subalgebras in \(U_q(\mathfrak{sl}_{n+1})\), Spherical functions on homogeneous superspaces, The center of quantum symmetric pair coideal subalgebras, Quantization of Poisson manifolds from the integrability of the modular function, Quantum homogeneous spaces with faithfully flat module structures, Quantum flag manifolds, quantum symmetric spaces and their associated universal \(K\)-matrices, Some remarks on the construction of quantum symmetric spaces, Quantum symmetric pairs and the reflection equation, Cartan subalgebras for quantum symmetric pair coideals, Coorbits of Quantum Homogeneous Spaces, Fourier transforms on the quantum \(\text{SU}(1,1)\) group. (With an appendix by Mizan Rahman).

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quantum 2-spheres and big q-Jacobi polynomials
• Askey-Wilson polynomials and the quantum group \(SU_ q(2)\)
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• Compact matrix pseudogroups
• Quantum spheres
• Quantum deformations of certain simple modules over enveloping algebras
• Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra
• Quantum homogeneous spaces, duality and quantum 2-spheres
• CQG algebras: A direct algebraic approach to compact quantum groups
• Macdonald's symmetric polynomials as zonal spherical functions on some quantum homogeneous spaces
• Algebra of functions on the quantum group SU(2)
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• Quantum G-spaces and Heisenberg algebra
• Grassmannian Legendre functions
• The Addition Formula for Continuousq-Legendre Polynomials and Associated Spherical Elements on the $SU(2)$ Quantum Group Related to Askey–Wilson Polynomials
• Askey–Wilson Polynomials as Zonal Spherical Functions on the ${\operatorname{SU}}(2)$ Quantum Group