Brauer's Height Zero Conjecture
We complete the proof of Brauer's Height Zero Conjecture from 1955 by establishing the open implication for all odd primes.
math.RT↗
arXiv subjects
Amanda A. Schaeffer Fry
Publications and source records attributed to Amanda A. Schaeffer Fry.
Finite groups with an irreducible character of large degree
Let $G$ be a finite group and $d$ the degree of a complex irreducible character of $G$, then write $|G|=d(d+e)$ where $e$ is a nonnegative integer. We prove that $|G|\leq e^4-e^3$ whenever $e>1$. This bound is best possible and improves on several earlier related results.
math.GR↗
$Sp_6(2^a)$ is "Good" for the McKay, Alperin Weight, and Related Local-Global Conjectures
The so-called "local-global" conjectures in the representation theory of finite groups relate the representation theory of $G$ to that of certain proper subgroups, such as the normalizers of particular $p$-groups. Recent results by several authors reduce some of these conjectures to showing that a certain collection of stronger conditions holds for all finite simple groups. Here, we show that $G=Sp_6(2^a)$ is "good" for these reductions for the McKay conjecture, the Alperin weight conjecture, and their blockwise versions.
math.GR↗
Cross-Characteristic Representations of $Sp_6(2^a)$ and Their Restrictions to Maximal Subgroups
We classify all pairs $(V,H)$, where $H$ is a proper subgroup of $G=Sp_6(q)$, $q$ even, and $V$ is an $\ell$-modular representation of $G$ for $\ell\neq 2$ which is absolutely irreducible as a representation of $H$. This problem is motivated by the Aschbacher-Scott program on classifying maximal subgroups of finite classical groups.
math.GR↗