An equivariant bijection between irreducible Brauer characters and weights for Sp(2n, q)
An equivariant bijection between irreducible Brauer characters and weights for Sp(2n, q)
复制标题
Sp(2n, q) 的不可约布劳尔特征和权重之间的等变双射
DOI：
10.1016/j.jalgebra.2019.07.031
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发表时间：
2019
影响因子：
0.9
通讯作者：
Li Conghui
中科院分区：
文献类型：
--
作者：
Li Conghui
The longstanding Alperin weight conjecture and its blockwise version have been reduced to simple groups recently by Navarro, Tiep, Späth 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 Sp 2 n (q) and odd non-defining characteristics. If the decomposition matrix of Sp 2 n (q) is unitriangular with respect to an Aut (Sp 2 n (q))-stable basic set (this assumption holds for linear primes), we can establish an equivariant bijection between the irreducible Brauer characters and weights.
