36 citations · 214 across the 29 of their papers we have counts for
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On the basic representation of the double affine Hecke algebra at critical level
J. F. van Diejen, E. Emsiz, I. N. Zurrián
We construct the basic representation of the double affine Hecke algebra at critical level associated to an irreducible reduced affine root system with a reduced gradient…
Affine Pieri rule for periodic Macdonald spherical functions and fusion rings
Jan Felipe van Diejen, Erdal Emsiz, Ignacio N. Zurrián
Let be an untwisted affine Lie algebra or the twisted counterpart thereof (which excludes the affine Lie algebras of type ). We pr…
Difference equation for the Heckman-Opdam hypergeometric function and its confluent Whittaker limit
J. F. van Diejen, E. Emsiz
We present an explicit difference equation for the Heckman-Opdam hypergeometric function associated with root systems. Via a confluent hypergeometric limit, an analogous difference…
Orthogonality of Macdonald polynomials with unitary parameters
J. F. van Diejen, E. Emsiz
For any admissible pair of irreducible reduced crystallographic root systems, we present discrete orthogonality relations for a finite-dimensional system of Macdonald polynomials w…
A discrete Fourier transform associated with the affine Hecke algebra
J. F. van Diejen, E. Emsiz
We introduce an explicit representation of the double affine Hecke algebra (of type ) at that gives rise to a periodic counterpart of a well-known Fourier transform asso…
Unitary representations of affine Hecke algebras related to Macdonald spherical functions
J. F. van Diejen, E. Emsiz
For any reduced crystallographic root system, we introduce a unitary representation of the (extended) affine Hecke algebra given by discrete difference-reflection operators acting…