The Capelli identity, the double commutant theorem and multiplicity-free-actions.
The Dunkl transform.
The structure of totally disconnected, locally compact groups.
Three results in Dunkl analysis
We first establish a geometric Paley-Wiener theorem for the Dunkl transform in the crystallographic case. Next we obtain an optimal bound for the norm of Dunkl translations in dimension 1. Finally, we describe more precisely the support of the distribution associated to Dunkl translations in higher dimension.
Total characters and Chebyshev polynomials.
Transformation properties of the generalized Muirhead operators