We construct a two-parameter family of actions ωk, a of the Lie algebra 𝔰𝔩 (2, ℝ) by
differential–difference operators on ℝN∖{0}. Here k is a multiplicity function for the Dunkl …

These lecture notes are intended as an introduction to the theory of rational Dunkl operators,
the associated special functions and related Markov processes with an emphasis on …

In this paper, we give some applications of the Dunkl-type Segal–Bargmann transform ℬ α in
the field of partial differential equations, such as the time-dependent Dunkl–Dirac Laplacian …

The classical Fischer decomposition of polynomials on Euclidean space makes it possible to
express any polynomial as a sum of harmonic polynomials multiplied by powers of| x| 2. A …

The study of spherical harmonics in superspace, introduced in (De Bie and Sommen 2007 J.
Phys. A: Math. Theor. 40 7193) is further elaborated. A detailed description of spherical …

In the present paper, a new family of integral transforms depending on two parameters and
related to the Dunkl transform is introduced. Well-known transforms, such as the fractional …

For a finite dimensional representation V of a finite reflection group W, we consider the
rational Cherednik algebra H t, c (V, W) associated with (V, W) at the parameters t≠ 0 and c …

For any Hermitian Lie group G of tube type we construct a Fock model of its minimal
representation. The Fock space is defined on the minimal nilpotent KC-orbit X in pC and the …

We study various aspects of the metaplectic Howe duality realized by the Fischer
decomposition for the metaplectic representation space of polynomials on R 2 n valued in …

Let k=(kα) αεℝ, be a positive-real valued multiplicity function related to a root system ℝ, and
Δk be the Dunkl-Laplacian operator. For (x, t) ε ℝN,× ℝ, denote by uk (x, t) the solution to the …