Bounding the number of characters in a block of a finite group

2018/07/22 by Benjamin Sambale, Sambale, Benjamin
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1807.08238

16 pages

arxiv created 2018/07/22 · arxiv updated 2018/07/24

Abstract

We present a strong upper bound on the number k(B) of irreducible characters of a p-block B of a finite group G in terms of local invariants. More precisely, the bound depends on a chosen major B-subsection (u,b), its normalizer N_G(⟨ u⟩,b) in the fusion system and a weighted sum of the Cartan invariants of b. In this way we strengthen and unify previous bounds given by Brauer, Wada, Külshammer--Wada, Héthelyi--Külshammer--Sambale and the present author.

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