Speaker: Jean Michel (Paris)
Title: Tower Equivalence and Lusztig's Fourier Transform
Chapuy and Douvropoulos, in the paper Coxeter factorizations with generalized Jucys-Murphy weights and Matrix Tree theorems for reflection groups, have defined a "tower equivalence" between characters of complex reflection groups. I found a connection between this notion and the Lusztig Fourier transform, defined by Lusztig for Weyl groups, and that with Broué and Malle we have extended to so-called spetsial reflection groups. This allows to give a uniform proof of the results of Chapuy and Douvropoulos for Weyl groups, and a conjectural similar proof for spetsial groups.