TY - JOUR

T1 - Bounding the number of characters in a block of a finite group

AU - Sambale, Benjamin

N1 - Funding Information: I have been pursuing these formulas since my PhD in 2010 and it has always remained a challenge to prove the most general. The work on this paper was initiated in February 2018 when I received an invitation by Christine Bessenrodt to the representation theory days in Hanover. I thank her for this invitation. The paper was written in summer 2018 while I was an interim professor at the University of Jena. I like to thank the mathematical institute for the hospitality and also my sister's family for letting me stay at their place. Moreover, I appreciate some comments on algebraic number theory by Tommy Hofmann. The work is supported by the German Research Foundation (projects SA 2864/1-1 and SA 2864/3-1). Funding Information: I have been pursuing these formulas since my PhD in 2010 and it has always remained a challenge to prove the most general. The work on this paper was initiated in February 2018 when I received an invitation by Christine Bessenrodt to the representation theory days in Hanover. I thank her for this invitation. The paper was written in summer 2018 while I was an interim professor at the University of Jena. I like to thank the mathematical institute for the hospitality and also my sister's family for letting me stay at their place. Moreover, I appreciate some comments on algebraic number theory by Tommy Hofmann. The work is supported by the German Research Foundation (projects SA 2864/1-1 and SA 2864/3-1 ).

PY - 2019/12/15

Y1 - 2019/12/15

N2 - 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 NG(〈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.

AB - 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 NG(〈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.

KW - Brauer's k(B)-Conjecture

KW - Cartan matrix

KW - Number of characters in a block

UR - http://www.scopus.com/inward/record.url?scp=85073514552&partnerID=8YFLogxK

U2 - https://doi.org/10.48550/arXiv.1807.08238

DO - https://doi.org/10.48550/arXiv.1807.08238

M3 - Article

AN - SCOPUS:85073514552

VL - 358

JO - Advances in mathematics

JF - Advances in mathematics

SN - 0001-8708

M1 - 106861

ER -