Quantum zonal spherical functions and Macdonald polynomials

DOI10.1016/j.aim.2003.11.007zbMath1127.17018arXivmath/0210447OpenAlexW1990118742MaRDI QIDQ1887448

Gail Letzter

Publication date: 26 November 2004

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0210447

zbMATH Keywords

quantum groupMacdonald polynomialzonal spherical function

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups (quantized function algebras) and their representations (20G42) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52) Harmonic analysis and spherical functions (43A90) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items (22)

The bar involution for quantum symmetric pairs ⋮ Properties of generalized univariate hypergeometric functions ⋮ Pairings and actions for dynamical quantum groups ⋮ Canonical bases arising from quantum symmetric pairs ⋮ Branching rules for finite-dimensional \(\mathcal {U}_{q}(\mathfrak {su}(3))\)-representations with respect to a right coideal subalgebra ⋮ Matrix-valued orthogonal polynomials related to the quantum analogue of \((\mathrm{SU}(2) \times \mathrm{SU}(2), \text{diag})\) ⋮ Non-Levi closed conjugacy classes of \(\mathrm{SP}_q(2n)\). ⋮ Quantum groups -- algebra, analysis and category theory. Abstracts from the workshop held September 12--18, 2021 (hybrid meeting) ⋮ Universal K-matrix for quantum symmetric pairs ⋮ Quantum symmetric Kac-Moody pairs ⋮ The dynamical \(U(n)\) quantum group ⋮ Non-Levi closed conjugacy classes of SO q(N) ⋮ The center of quantum symmetric pair coideal subalgebras ⋮ Quantum flag manifolds, quantum symmetric spaces and their associated universal \(K\)-matrices ⋮ Symmetric pairs for Nichols algebras of diagonal type via star products ⋮ Quantum symmetric pairs and the reflection equation ⋮ Book Review: Double affine Hecke algebras ⋮ Defining relations for quantum symmetric pair coideals of Kac-Moody type ⋮ Factorisation of quasi \(K\)-matrices for quantum symmetric pairs ⋮ Cartan subalgebras for quantum symmetric pair coideals ⋮ A bispectral q-hypergeometric basis for a class of quantum integrable models ⋮ Koornwinder polynomials and the \(XXZ\) spin chain

Cites Work

• Evaluation of the quantum affine PRV determinants
• Local finiteness of the adjoint action for quantized enveloping algebras
• A completion of the quantized enveloping algebra of a Kac-Moody algebra
• Quantum symmetric pairs and their zonal spherical functions.
• Orthogonal polynomials associated with root systems
• Some remarks on the construction of quantum symmetric spaces
• Macdonald's symmetric polynomials as zonal spherical functions on some quantum homogeneous spaces
• Symmetric pairs for quantized enveloping algebras
• Some limit transitions between BC type orthogonal polynomials interpreted on quantum complex Grassmannians
• A family of quantum projective spaces and related $q$-hypergeometric orthogonal polynomials
• Separation of Variables for Quantized Enveloping Algebras
• On a Harish-Chandra homomorphism
• Lectures on affine Hecke algebras and Macdonald’s conjectures
• Subalgebras Which Appear in Quantum Iwasawa Decompositions
• Askey–Wilson Polynomials as Zonal Spherical Functions on the ${\operatorname{SU}}(2)$ Quantum Group
• Fundamental Solutions of Invariant Differential Operators on Symmetric Spaces
• Introduction to Lie Algebras and Representation Theory
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