The representations of the degenerate affine Hecke algebra in which the analogues of the Dunkl operators are given by finite-difference operators are introduced. The non-selfadjoint lattice analogues of the spin Calogero-Sutherland hamiltonians are analysed by Bethe-Ansatz. The sl(m)-Yangian representations arising from the finite-difference representations of the degenerate affine Hecke algebr...

We construct special solutions to the rational quantum KnizhnikZamolodchikov equation associated with the Lie algebra glN . The main ingredient is a special class of the shifted non-symmetric Jack polynomials. It may be regarded as a shifted version of the singular polynomials studied by Dunkl. We conjecture that our solutions contain those obtained as a scaling limit of matrix elements of the ...

We prove a limit relation for the Dunkl–Bessel function of type BN with multiplicity parameters k1 on the roots ±ei and k2 on ±ei ± ej where k1 tends to infinity and the arguments are suitably scaled. It gives a good approximation in terms of the Dunkltype Bessel function of type AN−1 with multiplicity k2. For certain values of k2 an improved estimate is obtained from a corresponding limit rela...

Classical ellipsoidal and sphero-conal harmonics are polynomial solutions of the Laplace equation that can be expressed in terms of Lamé polynomials. Generalized ellipsoidal and sphero-conal harmonics are polynomial solutions of the more general Dunkl equation that can be expressed in terms of Stieltjes polynomials. Niven’s formula connecting ellipsoidal and sphero-conal harmonics is generalize...

where A and B are fixed polynomials with degA ≤ 2, and degB = 1. In 1939, Shohat extended these ideas introducing a new class of orthogonal polynomials. In fact, he studied orthogonal polynomials associated with forms satisfying the last equation, with no restrictions in the degrees of the polynomials A, and B. Obviously, orthogonal polynomials defined as above, generalize in a natural way the ...

Long term BVOC fluxes above mountain grassland I. Bamberger, L. Hörtnagl, R. Schnitzhofer, M. Graus, T. M. Ruuskanen, M. Müller, J. Dunkl, G. Wohlfahrt, and A. Hansel Institute of Ion Physics and Applied Physics, University of Innsbruck, Innsbruck, Austria Institute of Ecology, University of Innsbruck, Innsbruck, Austria currently at: IONICON ANALYTIK, Innsbruck, Austria Received: 19 November 2...

Recently a new technique in the harmonic analysis on symmetric spaces was suggested based on certain remarkable representations of affine and double affine Hecke algebras in terms of Dunkl and Demazure operators instead of Lie groups and Lie algebras. In the classic case (see [O,H,C5]) it resulted (among other applications) in a new theory of radial part of Laplace operators and their deformati...