Details
| Original language | English |
|---|---|
| Article number | 106861 |
| Journal | Advances in mathematics |
| Volume | 358 |
| Publication status | Published - 15 Dec 2019 |
| Externally published | Yes |
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 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.
Keywords
- Brauer's k(B)-Conjecture, Cartan matrix, Number of characters in a block
ASJC Scopus subject areas
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In: Advances in mathematics, Vol. 358, 106861, 15.12.2019.
Research output: Contribution to journal › Article › Research › peer review
}
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 -