Tower equivalence and Lusztig’s truncated Fourier transform

If f f denotes the truncated Lusztig Fourier transform, we show that image by of normalized characteristic function a Coxeter element is alternate sum exterior powers reflection representation, and any class tower equivalent to its . In particular this gives proof results Chapuy Douvropoulos on “Coxeter factorizations with generalized Jucys-Murphy weights matrix tree theorems for groups” irreducible spetsial groups, based Deligne-Lusztig combinatorics.