Nikolaus Conference 2021

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.

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