Dunkl operators, generalized Bessel functions and Hurwitz numbers

Vortrag von Prof. Dr. Nizar Demni

Sprecher eingeladen von: Prof. Dr. Valentin Féray

Datum: 16.04.18  Zeit: 14.00 - 14.45  Raum: Y27H26

I'll recall some facts on finite root systems needed to introduce Dunkl operators and give some remarkable properties of the latter. Then, I'll talk about the existence of the so-called Dunkl intertwining operator and its relation with the Harish-Chandra integral and generalized Bessel functions. Finally, I'll show how these functions may be expanded in terms of the Hurwitz numbers (number of factorizations of an element of the reflection group into a product of reflections) and give a special interest in the cases of dihedral and symmetric groups.