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Orthogonal Polynomials of Several Variables
  • J. Stokman
  • Computer Science, Mathematics
  • J. Approx. Theory
  • 31 October 2001
We report on the recent development on the general theory of orthogonal polynomials in several variables, in which results parallel to the theory in one variable are established using a vectormatrix notation. Expand
Askey-Wilson polynomials: an affine Hecke algebra approach
We study Askey-Wilson type polynomials using representation theory of the double affine Hecke algebra. In particular, we prove bi-orthogonality relations for non-symmetric and anti-symmetricExpand
The Askey-Wilson function transform
In this paper we present an explicit (rank one) function transform which contains several Jacobi-type function transforms and Hankel-type transforms as degenerate cases. The kernel of the transform,Expand
Some limit transitions between BC type orthogonal polynomials interpreted on quantum complex Grassmannians
The quantum complex Grassmannian U_q/K_q of rank l is the quotient of the quantum unitary group U_q=U_q(n) by the quantum subgroup K_q=U_q(n-l)xU_q(l). We show that (U_q,K_q) is a quantum GelfandExpand
Hyperbolic beta integrals
Abstract 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 viewed asExpand
Multivariable big and little q -Jacobi polynomials
A four-parameter family of multivariable big q-Jacobi polynomials and a three-parameter family of multivariable little q-Jacobi polynomials are introduced. For both families, full orthogonality isExpand
Multivariable q-Racah polynomials
The Koornwinder-Macdonald multivariable generalization of the Askey-Wilson polynomials is studied for parameters satisfying a truncation condition such that the orthogonality measure becomes discreteExpand
On BC type basic hypergeometric orthogonal polynomials
The five parameter family of multivariable Askey-Wilson polynomials is studied with four parameters generically complex. The multivariable Askey-Wilson polynomials form an orthogonal system withExpand
Koornwinder polynomials and affine Hecke algebras
In this paper we derive the bi-orthogonality relations, diagonal term evaluations and evaluation formulas for the non-symmetric Koornwinder polynomials. For the derivation we use certainExpand
Generalized Onsager Algebras
Let g(A)$\mathfrak {g}(A)$ be the Kac-Moody algebra with respect to a symmetrizable generalized Cartan matrix A. We give an explicit presentation of the fix-point Lie subalgebra k(A)$\mathfrakExpand