Speaker
Siddhartha Sahi, Rutgers, The State University of New Jersey
Abstract
“We prove that the Opdam–Cherednik kernel, also known as the nonsymmetric Opdam hypergeometric function, can be written as the Laplace transform of a positive measure supported on the convex hull of the Weyl group orbit of its argument. As a consequence, the trigonometric Dunkl intertwining operator is positivity preserving. The main ingredient in the proof is a new formula for the Opdam–Cherednik kernel as a degeneration of nonsymmetric Macdonald polynomials. As a further application, we prove majorization inequalities for Macdonald polynomials and Heckman–Opdam hypergeometric functions associated with arbitrary root systems.
This is joint work with Colin McSwiggen (Academia Sinica), arXiv:2606.15185“