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Mathematics > Representation Theory

arXiv:2207.08462 (math)
[Submitted on 18 Jul 2022 (v1), last revised 24 Apr 2023 (this version, v3)]

Title:Tower equivalence and Lusztig's truncated Fourier transform

Authors:Jean Michel (IMJ-PRG)
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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 .
Subjects: Representation Theory (math.RT)
Cite as: arXiv:2207.08462 [math.RT]
  (or arXiv:2207.08462v3 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.2207.08462

Submission history

From: Jean Michel [view email] [via CCSD proxy]
[v1] Mon, 18 Jul 2022 09:29:15 UTC (10 KB)
[v2] Thu, 1 Sep 2022 13:03:51 UTC (10 KB)
[v3] Mon, 24 Apr 2023 11:37:47 UTC (12 KB)
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