Related papers: On the inductive blockwise Alperin weight conditio…

We prove the Alperin-McKay Conjecture for all $p$-blocks of finite groups with metacyclic, minimal non-abelian defect groups. These are precisely the metacyclic groups whose derived subgroup have order $p$. In the special case $p=3$, we…

In this paper characters of the normaliser of $d$-split Levi subgroups in $\mathrm {SL}_n(q)$ and $\mathrm {SU}_n(q)$ are parametrized with a particular focus on the Clifford theory between the Levi subgroup and its normalizer.These results…

This paper is motivated by the study of Alperin's weight conjecture in the representation theory of finite groups. We generalize the notion of $e$-cuspidality in the $e$-Harish-Chandra theory of finite reductive groups, and define generic…

The so-called inductive McKay condition on finite simple groups, due to Isaacs-Malle-Navarro (2007), has been recently reformulated by Sp\"ath. We show that this reformulation applies to the reduction theorem for Alperin's weight…

As a sequel to [CS13b], we verify the so-called inductive AM-condition introduced in [Sp12] for simple groups of type A and blocks with maximal defect. This is part of the program set up to verify the Alperin-McKay conjecture through its…

Let $k$ be an algebraically closed field of positive characteristic $p$ and let $\mathbb{F}$ be an algebraically closed field of characteristic 0. We consider Alperin's weight conjecture (over $k$) from the point of view of (stable)…

Sp\"ath showed that the Alperin-McKay conjecture in the representation theory of finite groups holds if the so-called inductive Alperin-McKay condition holds for all finite simple groups. In a previous article, we showed that the…

This paper is concerned with the representation theory of finite groups. According to Robinson, the truth of certain variants of Alperin's weight conjecture on the $p$-blocks of a finite group would imply some arithmetical conditions on the…

We verify the inductive blockwise Alperin weight condition in odd characteristic $\ell$ for the finite exceptional Chevalley groups $F_4(q)$ for $q$ not divisible by $\ell$.

The Alperin-McKay conjecture is a longstanding open conjecture in the representation theory of finite groups. Sp\"ath showed that the Alperin-McKay conjecture holds if the so-called inductive Alperin-McKay (iAM) condition holds for all…

Fundamental conjectures in modular representation theory of finite groups, more precisely, Alperin's Weight Conjecture and Robinson's Ordinary Weight Conjecture, can be expressed in terms of fusion systems. We use fusion systems to connect…

In a finite group G, we consider nilpotent weights, and prove a pi-version of the Alperin Weight Conjecture for certain pi-separable groups. This widely generalizes an earlier result by I. M. Isaacs and the first author.

We prove analogues for reductive algebraic groups of some results for finite groups due to Knoerr and Robinson which play a central role in their reformulation of Alperin's conjecture for finite groups.

The Alperin weight conjecture has been reduced to simple groups by Navarro and Tiep. In this paper, we investigate the Navarro Alperin weight conjecture, which includes Galois automorphisms and group automorphisms in comparison with the…

In this paper we consider the inductive Alperin-McKay condition for quasi-isolated 2-blocks of exceptional groups of Lie type. Thereby, we complete the proof of the Alperin-McKay conjecture for the prime 2.

We show that Brauer's height zero conjecture holds for blocks of finite quasi-simple groups. This result is used in Navarro-Sp\"ath's reduction of this conjecture for general groups to the inductive Alperin-McKay condition for simple…

We prove that Brauer's Height Zero Conjecture holds for p-blocks of finite groups with metacyclic defect groups. If the defect group is nonabelian and contains a cyclic maximal subgroup, we obtain the distribution into p-conjugate and…

In this paper we propose a conjecture concerning partial sums of an arbitrary finite subset of an abelian group, that naturally arises investigating simple Heffter systems. Then, we show its connection with related open problems and we…

In this paper we consider the inductive Alperin--McKay condition for isolated blocks of groups of Lie type $B$ and $C$. This finishes the verification of the inductive condition for groups of this type.

Let $p$ be a prime, $k$ an algebraic closure of $\mathbb{F}_p$ and $\Gamma$ the Galois group ${\rm Gal}(k/\mathbb{F}_p)$. Let $\mathcal{C}$ be a finite category and $\mathcal{O}_{\mathcal{C}}$ the $p$-orbit category of $\mathcal{C}$ defined…