Perfect generalized characters inducing the Alperin-McKay conjecture
Perfect generalized characters inducing the Alperin-McKay conjecture
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导出阿尔珀林-麦凯猜想的完美广义特征
DOI：
10.1016/j.jalgebra.2008.05.031
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发表时间：
2008
影响因子：
0.9
通讯作者：
Charles W. Eaton
中科院分区：
文献类型：
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作者：
Charles W. Eaton
众所周知，当缺陷群是非阿贝尔的时，Broué的S猜想中预测的完美等距线并不总是存在的，即使当块具有等价的Brauer范畴时也是如此。我们考虑在缺陷群的正规化子中诱导块的高度为零的不可约特征标集与其Brauer对应的不可约特征标集之间的双射的完全广义特征标，从而为Alperin-McKay猜想中预测的数值重合提供了一种‘解释’。这样，推广了Broué的S猜想中所预言的具有阿贝尔缺陷群的块的完美等距线。虽然这种广义特征标一般不存在，但我们证明了当亏群是p3阶的非交换平凡交子群时，以及对于q的2的幂的B22(Q)和所有q的PSU3(Q)，它们确实存在。此外，我们还证明了这些块满足广义形式的同型。
It is well known that the perfect isometries predicted in Broué's conjecture do not always exist when the defect groups are non-abelian, even when the blocks have equivalent Brauer categories. We consider perfect generalized characters which induce bijections between the sets of irreducible characters of height zero of a block and of its Brauer correspondent in the normalizer of a defect group, hence providing in these cases an ‘explanation’ for the numerical coincidence predicted in the Alperin–McKay conjecture. In this way the perfect isometries predicted in Broué's conjecture for blocks with abelian defect groups are generalized. Whilst such generalized characters do not exist in general, we show that they do exist when the defect groups are non-abelian trivial intersection subgroups of order p3, as well as for B22(q) for q a power of two and PSU3(q) for all q. Further, we show that these blocks satisfy a generalized version of an isotypy.