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Zhicheng Feng

Publications and source records attributed to Zhicheng Feng.

22 records · Page 2Linked to original sources
arXiv2021

Inductive blockwise Alperin weight condition for type B and odd primes

By the reduction theorems of Navarro--Tiep and Späth, a way to prove the Alperin weight conjecture and its blockwise version is to verify the co-called inductive Alperin weight condition and inductive blockwise Alperin weight condition for all finie simple groups respectively. In this paper, we establish the inductive blockwise Alperin weight condition for simple groups of type $\mathsf B$ and odd primes, using a criterion given by Brough and Späth recently.

math.RT↗
arXiv2020

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

We establish the inductive blockwise Alperin weight condition for simple groups of Lie type $\mathsf C$ and the bad prime $2$. As a main step, we derive a labelling set for the irreducible $2$-Brauer characters of the finite symplectic groups Sp$_{2n}(q)$ (with odd $q$), together with the action of automorphisms. As a further important ingredient we prove a Jordan decomposition for weights.

math.RT↗
arXiv2019

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 $\ell$-block of $SL_n(εq)$ if $\ell\nmid\mathrm{gcd}(n,q-ε)$.

math.RT↗