Results 1  10
of
13
The cfunction expansion of a basic hypergeometric function associated to root systems
 I. Cherednik) Department of Mathematics, UNC Chapel Hill, North Carolina 27599
"... ar ..."
(Show Context)
Orthogonality relations and Cherednik identities for multivariable Baker–Akhiezer functions
"... We establish orthogonality relations for the Baker–Akhiezer (BA) eigenfunctions of the Macdonald difference operators. We also obtain a version of Cherednik–Macdonald–Mehta integral for these functions. As a corollary, we give a simple derivation of the norm identity and Cherednik–Macdonald–Mehta in ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
We establish orthogonality relations for the Baker–Akhiezer (BA) eigenfunctions of the Macdonald difference operators. We also obtain a version of Cherednik–Macdonald–Mehta integral for these functions. As a corollary, we give a simple derivation of the norm identity and Cherednik–Macdonald–Mehta integral for Macdonald polynomials. In the appendix written by the first author, we prove a summation formula for BA functions. We also consider more general identities of Cherednik type, which we use to introduce and construct more general, twisted BA functions. This leads to a construction of new quantum integrable models of Macdonald–Ruijsenaars type.
Quantum affine KnizhnikZamolodchikov equations and quantum spherical functions, I
, 2010
"... ..."
(Show Context)
Some Remarks on VeryWellPoised 8φ7 Series
"... Abstract. Nonpolynomial basic hypergeometric eigenfunctions of the Askey–Wilson second order difference operator are known to be expressible as verywellpoised 8φ7 series. In this paper we use this fact to derive various basic hypergeometric and theta function identities. We relate most of them to ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
(Show Context)
Abstract. Nonpolynomial basic hypergeometric eigenfunctions of the Askey–Wilson second order difference operator are known to be expressible as verywellpoised 8φ7 series. In this paper we use this fact to derive various basic hypergeometric and theta function identities. We relate most of them to identities from the existing literature on basic hypergeometric series. This leads for example to a new derivation of a known quadratic transformation formula for verywellpoised 8φ7 series. We also provide a link to Chalykh’s theory on (rank one, BC type) Baker–Akhiezer functions. Key words: verywellpoised basic hypergeometric series; Askey–Wilson functions; quadratic transformation formulas; theta functions 2010 Mathematics Subject Classification: 33D15; 33D45 1
doi:10.1093/imrn/rnt076 Joint Eigenfunctions for the Relativistic Calogero–Moser Hamiltonians of Hyperbolic Type: I. First Steps
, 2013
"... We present and develop a recursion scheme to construct joint eigenfunctions for the commuting analytic difference operators associated with the integrable Nparticle systems of hyperbolic relativistic Calogero–Moser type. The scheme is based on kernel identities we obtained in previous work. In th ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
(Show Context)
We present and develop a recursion scheme to construct joint eigenfunctions for the commuting analytic difference operators associated with the integrable Nparticle systems of hyperbolic relativistic Calogero–Moser type. The scheme is based on kernel identities we obtained in previous work. In this first paper of a series, we present the formal features of the scheme, show explicitly its arbitraryN viability for the “free ” cases, and supply the analytic tools to prove the joint eigenfunction properties in suitable holomorphy domains. 1
DIFFERENTIAL EQUATIONS COMPATIBLE WITH BOUNDARY RATIONAL QKZ EQUATION
, 908
"... Dedicated to Professor Tetsuji Miwa on his sixtieth birthday Abstract. We give differential equations compatible with the rational qKZ equation with boundary reflection. The total system contains the trigonometric degeneration of the bispectral qKZ equation of type (C ∨ n, Cn) which in the case of t ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Dedicated to Professor Tetsuji Miwa on his sixtieth birthday Abstract. We give differential equations compatible with the rational qKZ equation with boundary reflection. The total system contains the trigonometric degeneration of the bispectral qKZ equation of type (C ∨ n, Cn) which in the case of type GLn was studied by van Meer and Stokman. We construct an integral formula for solutions to our compatible system in a special case. 1.
Connection Problems for Quantum Affine KZ Equations and Integrable Lattice Models
"... Link to publication Citation for published version (APA): Stokman, J. V. (2015). Connection Problems for Quantum Affine KZ Equations and Integrable Lattice Models. Communications in Mathematical Physics, 338(3), 13631409. https://doi.org/10.1007/s002200152375z General rights It is not permitted ..."
Abstract
 Add to MetaCart
(Show Context)
Link to publication Citation for published version (APA): Stokman, J. V. (2015). Connection Problems for Quantum Affine KZ Equations and Integrable Lattice Models. Communications in Mathematical Physics, 338(3), 13631409. https://doi.org/10.1007/s002200152375z General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Download date: 01 Jul 2019 Digital Object Identifier (DOI) 10.1007/s002200152375z Commun. Math. Phys. 338, 13631409 For the spin representation of the affine Hecke algebra of type C, the quantum affine KZ equations become the boundary qKZ equations associated to the Heisenberg spin1 2 XXZ chain. We show that in this special case the results lead to an explicit 4parameter family of elliptic solutions of the dynamical reflection equation associated to Baxter's 8vertex face dynamical Rmatrix. We use these solutions to define an explicit 9parameter elliptic family of boundary quantum KnizhnikZamolodchikovBernard (KZB) equations.