Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications

Abstract

A unified approach is given to kernel functions which intertwine Ruijsenaars difference operators of type A and of type BC. As an application of the trigonometric cases, new explicit formulas for Koornwinder polynomials attached to single columns and single rows are derived.

40 pages. Three sections are added in Appendix, as well as several comments and references

References in corpus (5)

• Self-dual Koornwinder-Macdonald polynomials
• Remarkable identities related to the (quantum) elliptic Calogero-Sutherland model
• Raising operators of row type for Macdonald polynomials
• $q$-Difference raising operators for Macdonald polynomials and the integrality of transition coefficients
• Some conjectures for Macdonald polynomials of type B, C, D

Cited by in corpus (27)

• Kernel functions and Bäcklund transformations for relativistic Calogero-Moser and Toda systems
• A Relativistic Conical Function and its Whittaker Limits
• Elliptic Virasoro Conformal Blocks
• Hilbert-Schmidt Operators vs. Integrable Systems of Elliptic Calogero-Moser Type IV. The Relativistic Heun (van Diejen) Case
• Source identity and kernel functions for elliptic Calogero-Sutherland type systems
• Elliptic Ding-Iohara Algebra and the Free Field Realization of the Elliptic Macdonald Operator
• Construction of eigenfunctions for the elliptic Ruijsenaars difference operators
• Source identity and kernel functions for Inozemtsev-type systems
• Difference operators of Sklyanin and van Diejen type
• The Elliptic Painlevé Lax Equation vs. van Diejen's 8-Coupling Elliptic Hamiltonian
• Commutative Families of the Elliptic Macdonald Operator
• An infinite family of higher-order difference operators that commute with Ruijsenaars operators of type $A$
• Source identities and kernel functions for deformed (quantum) Ruijsenaars models
• Branching Formula for Macdonald-Koornwinder Polynomials
• Spectrum and eigenfunctions of the lattice hyperbolic Ruijsenaars-Schneider system with exponential Morse term
• A generalization of the Sears--Slater transformation and elliptic Lagrange interpolation of type $B{C}_n$
• Elliptic Ding-Iohara Algebra and Commutative Families of the Elliptic Macdonald Operator
• Ground state wavefunctions of elliptic relativistic integrable Hamiltonians
• Connection Formula for the Jackson Integral of Type $A_n$ and Elliptic Lagrange Interpolation
• Series Solutions of the Non-Stationary Heun Equation
• Quantum Integrals for a Semi-Infinite $q$-Boson System with Boundary Interactions
• Branching Rules for Symmetric Hypergeometric Polynomials
• A determinant formula associated with the elliptic hypergeometric integrals of type $B{C}_n$
• Macdonald Polynomials of Type $C_n$ with One-Column Diagrams and Deformed Catalan Numbers
• Some transformation formulas associated with Askey-Wilson polynomials and Lassalle's formulas for Macdonald-Koornwinder polynomials
• On R-matrix identities related to elliptic anisotropic spin Ruijsenaars-Macdonald operators
• Kernel identities for van Diejen's $q$-difference operators and transformation formulas for multiple basic hypergeometric series