Macdonald polynomials and algebraic integrability

DOI10.1006/aima.2001.2033zbMath1004.33009arXivmath/0212313OpenAlexW2055546524MaRDI QIDQ1599837

Oleg A. Chalykh

Publication date: 3 February 2003

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

Full work available at URL: https://arxiv.org/abs/math/0212313

zbMATH Keywords

Baker-Akhiezer functionMacdonald polynomialsalgebraic integrabilityMacdonald conjecturesMacdonald operatorsdeformed Macdonald-Ruijsenaars operatorKoornwinder operator

Mathematics Subject Classification ID

Groups and algebras in quantum theory and relations with integrable systems (81R12) Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items

Deformed Macdonald-Ruijsenaars operators and super Macdonald polynomials, Higher order deformed elliptic Ruijsenaars operators, Orthogonality of Macdonald polynomials with unitary parameters, On Cohen-Macaulayness of algebras generated by generalized power sums. With an appendix by Misha Feigin, Multiplicative quiver varieties and generalised Ruijsenaars-Schneider models, Orthogonality relations and Cherednik identities for multivariable Baker-Akhiezer functions, Source identities and kernel functions for deformed (quantum) Ruijsenaars models, Poisson-Lie interpretation of trigonometric Ruijsenaars duality, Toward explicit Hilbert series of quasi-invariant polynomials in characteristic \(p\) and \(q\)-deformed quasi-invariants, The research and progress of the enumeration of lattice paths, Macdonald duality and the proof of the quantum Q-system conjecture, Generalized Macdonald-Ruijsenaars systems., Connection coefficients for basic Harish-Chandra series, An asymptotic formula for the Koornwinder polynomials, ON THE QUANTUM RUIJSENAARS MODEL, SOME QUANTUM HOMOGENEOUS SPACES AND HECKE ALGEBRAS, Refined Chern-Simons theory and \((q, t)\)-deformed Yang-Mills theory: semi-classical expansion and planar limit, Pieri Formulae and Specialisation of Super Jacobi Polynomials, Bispectral commuting difference operators for multivariable Askey-Wilson polynomials, From Kajihara's transformation formula to deformed Macdonald-Ruijsenaars and Noumi-Sano operators, Difference equations and Pieri formulas for \(G_2\) type Macdonald polynomials and integrability, Orthogonality and the qKZB-heat equation for traces of \(U_q({\mathfrak g})\)-intertwiners

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Differential equations in the spectral parameter
• Some applications of hypergeometric shift operators
• Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
• Collisions of Calogero-Moser particles and an adelic Grassmannian (with an appendix by I. G. Macdonald)
• Constant term identities, orthogonal polynomials and affine Hecke algebras
• Algebraic integrability for the Schrödinger equation and finite reflection groups
• Residue construction of Hecke algebras
• Nonsymmetric Koornwinder polynomials and duality
• Commutative rings of partial differential operators and Lie algebras
• Double affine Hecke algebras and Macdonald's conjectures
• Macdonald's polynomials and representations of quantum groups
• A unified representation-theoretic approach to special functions
• Macdonald's evaluation conjectures and difference Fourier transform
• Multidimensional Baker-Akhiezer functions and Huygens' principle
• Affine root systems and Dedekind's \(\eta\)-function
• An elementary approach to the hypergeometric shift operators of Opdam
• Bispectrality for the quantum Ruijsenaars model and its integrable deformation
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
• On Cherednik-Macdonald-Mehta identities
• The duality of the generalized Calogero and Ruijsenaars problems
• New integrable deformations of the Calogero-Moser quantum problem
• Lectures on affine Hecke algebras and Macdonald’s conjectures
• Commuting difference operators with polynomial eigenfunctions
• Erratum: Solution of the one-dimensional N-body problems with quadratic and/or inversely quadratic pair potentials [J. Math. Phys. 12, 419–436 (1971)]
• On an inner product in modular tensor categories
• Self-dual Koornwinder-Macdonald polynomials