A Laplace-type representation of the generalized spherical functions associated to the root systems of type A
Representation Theory
2016-08-12 v1
Abstract
In this paper, we extend the iterative expression for the generalized spherical functions associated to the root systems of type previously obtained beyond regular elements. We also provide the corresponding expression in the flat case. From there, we derive a Laplace-type representation for the generalized spherical functions associated to the root systems of type in the Dunkl setting as well as in the trigonometric Dunkl setting. This representation leads us to describe precisely the support of the generalized Abel transform. Thanks to a recent result of Rejeb, this allows us to give the support for the Dunkl intertwining operator.
Keywords
Cite
@article{arxiv.1608.03567,
title = {A Laplace-type representation of the generalized spherical functions associated to the root systems of type A},
author = {Patrice Sawyer},
journal= {arXiv preprint arXiv:1608.03567},
year = {2016}
}