English

Tower equivalence and Lusztig's truncated Fourier transform

Representation Theory 2023-04-25 v3

Abstract

We give a proof of the results of Chapuy and Douvropoulos [3] for irreducible spetsial reflection groups based on Deligne-Lusztig combinatorics. In particular, if f denotes the truncated Lusztig Fourier transform, we show that the image by f of the normalized characteristic function of a Coxeter element is the alternate sum of the exterior powers of the reflection representation, and that a class function is tower equivalent to its image by f .

Keywords

Cite

@article{arxiv.2207.08462,
  title  = {Tower equivalence and Lusztig's truncated Fourier transform},
  author = {Jean Michel},
  journal= {arXiv preprint arXiv:2207.08462},
  year   = {2023}
}