Character correspondences for symmetric groups and wreath products
Character correspondences for symmetric groups and wreath products
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对称群和花环积的字符对应
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
A. Evseev
中科院分区：
文献类型：
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作者：
A. Evseev
Alperin—McKay猜想将任意有限群的块的不可约性质与它的$p$局部子群的不可约性质联系起来。作者在以前的一篇论文中对这个猜想作了进一步的阐述。我们证明了这种细化对对称群的所有块都成立。在此过程中，我们确定了$S_{pw}$的主块与$S_p\wr S_w$的主块之间的“规范”等距。我们还证明了用某些诱导字符表示环积虚字符的一个一般定理。本文将具有阿贝尔缺陷的对称群的块和相关环积的特征论结果推广到任意缺陷的情况。
The Alperin--McKay conjecture relates irreducible characters of a block of an arbitrary finite group to those of its $p$-local subgroups. A refinement of this conjecture was stated by the author in a previous paper. We prove that this refinement holds for all blocks of symmetric groups. Along the way we identify a "canonical" isometry between the principal block of $S_{pw}$ and that of $S_p\wr S_w$. We also prove a general theorem on expressing virtual characters of wreath products in terms of certain induced characters. Much of the paper generalises character-theoretic results on blocks of symmetric groups with abelian defect and related wreath products to the case of arbitrary defect.
麦凯猜想和布劳尔归纳定理
影响因子：
1.8
作者：
Evseev A
通讯作者：
Evseev A