arXiv subjects

Ruwen Hollenbach

Publications and source records attributed to Ruwen Hollenbach.

3 recordsLinked to original sources

arXiv2021

On $e$-cuspidal pairs of finite groups of exceptional Lie Type

Let $G$ be a simple, simply connected algebraic group of exceptional type defined over $\mathbb{F}_q$ with Frobenius endomorphism $F: G \to G$. Let $\ell \nmid q$ be a good prime for $G$. We determine the number of irreducible Brauer characters in the quasi-isolated $\ell$-blocks of $G^F$. This is done by proving that generalized $e$-Harish-Chandra theory holds for the Lusztig series associated to quasi-isolated elements of $G^{*F}$.

math.RT↗

arXiv2020

The centralizer of a Coxeter element

We prove that the centralizer of a Coxeter element in an irreducible Coxeter group is the cyclic group generated by that Coxeter element.

math.GR↗

arXiv2019

Bounds on the number of simple modules in blocks of finite groups of Lie type

Let $G$ be a simple, simply connected linear algebraic group of exceptional type defined over $\mathbb{F}_q$ with Frobenius endomorphism $F: G \to G$. In this work we give upper bounds on the number of simple modules in the quasi-isolated $\ell$-blocks of $G^F$ and $G^F/Z(G^F)$ when $\ell$ is bad for $G$.

math.RT↗