The inductive blockwise Alperin weight condition for type $\mathsf C$ and the prime $2$

对称群与交错群双重覆盖的分块 Navarro Alperin 权猜想

The Blockwise Navarro Alperin Weight Conjecture for Double Covers of Symmetric and Alternating Groups

本文证明了对称群与交错群双重覆盖的分块 Navarro Alperin 权猜想。

On the inductive blockwise Alperin weight condition for type $\mathsf A$

In this paper we prove the blockwise Alperin weight conjecture for finite special linear and unitary groups, for finite groups with abelian Sylow $3$-subgroups, and verify the inductive blockwise Alperin weight condition for certain cases of groups of type $\mathsf A$. We also give a classification for the 2-blocks of special linear and unitary groups.

Morita equivalences and the inductive blockwise Alperin weight condition for type $\mathsf A$

As a step to establish the blockwise Alperin weight conjecture for all finite groups, we verify the inductive blockwise Alperin weight condition introduced by Navarro--Tiep and Späth for simple groups of Lie type $\mathsf A$, split or twisted. Key to the proofs is to reduce the verification of the inductive condition to the isolated (that means unipotent) blocks, using the Jordan decomposition for blocks of finite reductive groups given by Bonnafé, Dat and Rouquier.

Jordan decomposition for weights and the blockwise Alperin weight conjecture

The Alperin weight conjecture was reduced to simple groups by the work of Navarro, Tiep and Späth. To prove Alperin weight conjecture, it suffices to show that all finite non-abelian simple groups are BAW-good. We reduce the verification of the inductive conditons for groups of Lie type in non-defining characteristic to quasi-isolated blocks.

Equivariant correspondences and the inductive Alperin weight condition for type $\mathsf A$

In this paper, we establish the inductive Alperin weight condition for the finite simple groups of Lie type $\mathsf A$, contributing to the program to prove the Alperin weight conjecture by checking the inductive condition for all finite simple groups.

A criterion for the inductive Alperin weight condition

We give a criterion that simplifies the checking of the inductive Alperin weight condition for the remaining open cases of simple groups of Lie type. It is strongly related in form to the criterion of the second author for the inductive McKay conditions (see [Spä12,2.12]) that has proved very useful. The proof follows from a Clifford theory for weights intrinsically present in the proof of reduction theorems of the Alperin weight conjecture given by Navarro--Tiep and the second author. We also give a related criterion for the inductive blockwise Alperin weight condition.

有限约化群的根子群

Radical subgroups of finite reductive groups

本文提出统一方法分类有限约化群的根$p$-子群，并验证其归纳分块Alperin权条件，应用于经典群与$F_4$型群，推进Alperin权猜想的证明。

关于类型 $\mathsf B$ 和类型 $\mathsf C$ 的归纳分块 Alperin 权条件的证明

On the inductive blockwise Alperin weight condition for type $\mathsf B$ and type $\mathsf C$

本文证明类型 B 和 C 的有限单群满足归纳分块 Alperin 权条件，通过置换格、Jordan 约化等方法去除单位三角假设，并补全散在群情形，从而推出相关群的块权猜想成立。

阿尔佩林重量猜想与盖拉布曼对应关系 via 特征标三元组

The Alperin Weight Conjecture and the Glauberman correspondence via character triples

本文通过特征标三元组验证了纳瓦罗猜想，并将其简化为单列群问题，证明了若干类群和块的结论。

阿尔佩林重量猜想、伽罗瓦自同构、交替和与函子等价

Alperin's weight conjecture, Galois automorphisms, alternating sums, and functorial equivalences

本文通过函子等价方法，证明了块级伽罗瓦阿尔佩林重量猜想的等价性，并探讨了伽罗瓦共轭块的函子等价性。

An equivariant bijection between irreducible Brauer characters and weights for Sp(2n, q)

The longstanding Alperin weight conjecture and its blockwise version have been reduced to simple groups recently by Navarro, Tiep, Spaeth and Koshitani. Thus, to prove this conjecture, it suffices to verify the corresponding inductive condition for all finite simple groups. The first is to establish an equivariant bijection between irreducible Brauer characters and weights for the universal covering groups of simple groups. Assume q is a power of some odd prime p. We first prove the blockwise Alperin weight conjecture for Sp2n(q) and odd non-defining characteristics. If the decomposition matri…

有限范畴代数的伽罗瓦阿尔佩林权重猜想

The Galois Alperin weight conjecture for finite category algebras

本文提出有限范畴代数的伽罗瓦阿尔佩林权重猜想，将其转化为有限群问题，并针对EI范畴提出块级猜想。

The blocks and weights of finite special linear and unitary groups

This paper has two main parts. Firstly, we give a classification of the $\ell$-blocks of finite special linear and unitary groups $SL_n(εq)$ in the non-defining characteristic $\ell\ge 3$. Secondly, we describe how the $\ell$-weights of $SL_n(εq)$ can be obtained from the $\ell$-weights of $GL_n(εq)$ when $\ell\nmid\mathrm{gcd}(n,q-ε)$, and verify the Alperin weight conjecture for $SL_n(εq)$ under the condition $\ell\nmid\mathrm{gcd}(n,q-ε)$. As a step to establish the Alperin weight conjecture for all finite groups, we prove the inductive blockwise Alperin weight condition for any unipotent $…

Alperin 界与正规 Sylow 子群

Alperin's bound and normal Sylow subgroups

本文将关于 $p$-Brauer 特征标数量与 Sylow $p$-子群正规性的猜想归约到有限单群并证明 $p=2$ 情形，同时建立 Alperin 下界分块版本的归约定理。

诱导块的Clifford特征标理论

Clifford theory of characters in induced blocks

我们给出了一个新的判定有限群的特征标是否扩张的准则。设$G$是有限群，$p$是素数.对于$N\lhd G$，我们考虑$p$ -$N$和${\rm N}_N(D)$的$b$和$b'$块，分别具有$(b')^N=b$，其中$D$是$b'$的缺陷组。在假定$G$与Dade在70年代初引入的$G$的正规子群$G[b]$重合的条件下，给出了$ϕ^G$与$(ϕ')^{{\rm N}_G(D)}$的所有不可约分支的集合之间的特征标对应，其中$ϕ$和$ϕ'$分别是$b$和$b'$的不可约Brauer特征标.这意味着哈里斯-克诺尔定理的一种推广。一个重要的工具是某些扩展的存在，这些扩展也有助于检查归纳Alperin-McKay和归纳Bessel Alperin Weight条件。

伽罗华自同构与块覆盖单幂块

Galois automorphisms and blocks covering unipotent blocks

本文证明了有限简单群中关于特征值延伸的条件成立，从而为有限群具有正常ℓ-补提供了新特征化，并研究了单幂块的特征分布及块级Galois-McKay猜想。