A family of tridiagonal pairs related to the quantum affine algebra .
A weighted Plancherel formula II. The case of the ball
The group SU(1,d) acts naturally on the Hilbert space , where B is the unit ball of and the weighted measure . It is proved that the irreducible decomposition of the space has finitely many discrete parts and a continuous part. Each discrete part corresponds to a zero of the generalized Harish-Chandra c-function in the lower half plane. The discrete parts are studied via invariant Cauchy-Riemann operators. The representations on the discrete parts are equivalent to actions on some holomorphic...
Critical points of the product of powers of linear functions and families of bases of singular vectors
Degenerate series representations of the -deformed algebra .
Double affine Hecke algebras of rank 1 and the -symmetric Askey-Wilson relations.
Dual pairs, spherical harmonics and a Capelli identity in quantum group theory
Duality of -polynomials, orthogonal on countable sets of points.
Dynamical matrices of elliptic quantum groups and connection matrices for the -KZ equations.
From double Hecke algebra to analysis.
Generalizations of Milne’s -Chu-Vandermonde summation
We derive two identities for multiple basic hyper-geometric series associated with the unitary group. In order to get the two identities, we first present two known -exponential operator identities which were established in our earlier paper. From the two identities and combining them with the two -Chu-Vandermonde summations established by Milne, we arrive at our...
Harmonic analysis on quantum spheres associated with representations of and -jacobi polynomials
Hermite -polynomials and -oscillators
Multivariable -Hahn polynomials as coupling coefficients for quantum algebra representations.
Nonsymmetric Koornwinder polynomials and duality.
On -analogs of recursions for the number of involutions and prime order elements in symmetric groups.
-orthogonal polynomials related to the quantum group .
Quantum algebras and associated with certain -Hahn polynomials: a revisited approach.
Raising and lowering operators for Askey-Wilson polynomials.
Représentations de dimension finie de l’algèbre de Cherednik rationnelle
On donne une condition nécessaire et suffisante pour l’existence de modules de dimension finie sur l’algèbre de Cherednik rationnelle associée à un système de racines.
Spherical functions on a complex classical quantum group