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8 papers · 1 filter
Right coideal subalgebras of the Borel part of a quantized enveloping algebra
I. Heckenberger, S. Kolb
For the Borel part of a quantized enveloping algebra we classify all right coideal subalgebras for which the intersection with the coradical is a Hopf algebra. The result is expres…
Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra
Tom H. Koornwinder
This paper builds on the previous paper arXiv:math/0612730 by the author, where a relationship between Zhedanov's algebra AW(3) and the double affine Hecke algebra (DAHA) correspon…
Generalized Cherednik-Macdonald identities
Jasper V. Stokman
We derive generalizations of the Cherednik-Macdonald constant term identities associated to root systems which depend, besides on the usual multiplicity function, symmetrically on…
Ruijsenaars' hypergeometric function and the modular double of U_q(sl(2,C))
Fokko J. van de Bult
Simultaneous eigenfunctions of two Askey-Wilson second order difference operators are constructed as formal matrix coefficients of the principal series representation of the modula…
Vertex-IRF transformations, dynamical quantum groups and harmonic analysis
Jasper V. Stokman
It is shown that a dynamical quantum group arising from a vertex-IRF transformation has a second realization with untwisted dynamical multiplication but nontrivial bigrading. Appli…
Hyperbolic beta integrals
Jasper V. Stokman
Hyperbolic beta integrals are analogues of Euler's beta integral in which the role of Euler's gamma function is taken over by Ruijsenaars' hyperbolic gamma function. They may be vi…