The formula is relative to the choice of a weighting system, that corresponds to the choice of $n$ free scalar parameters and of a parabolic tower of subgroups. This leads us to introduce (a class of) variants of the Jucys-Murphy elements for every group, from which we define a new notion of "tower equivalence" of virtual characters. The main technical point is to prove the tower equivalence between virtual characters naturally appearing in the problem, and exterior products of the reflection representation.

Received: November 20, 2019. Accepted: February 20, 2020. Final version: April 30, 2020.

The following versions are available:

- PDF (189 K)
- TeX version