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arXiv · 2207.08462

Tower equivalence and Lusztig's truncated Fourier transform

Jean Michel
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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 .

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Jean Michel. 2023-04-24. Tower equivalence and Lusztig's truncated Fourier transform. https://arxiv.org/abs/2207.08462

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