Restriction of Odd Degree Characters and Natural Correspondences
Restriction of Odd Degree Characters and Natural Correspondences
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奇数度字符和自然对应的限制
DOI：
10.1093/imrn/rnw174
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发表时间：
2017
影响因子：
1
通讯作者：
Tiep, Pham Huu
中科院分区：
文献类型：
--
作者：
Giannelli, Eugenio;Kleshchev, Alexander;Navarro, Gabriel;Tiep, Pham Huu
设是一个奇素数幂，我们限制的奇数度不可约字符，以发现一个自然的对应字符，为和。对于某些具有自正规Sylow-子群的有限群，也得到了类似的结果。其次，我们构造了一个典型的双射之间的奇度不可约字符，或与奇，和那些，其中是一个Sylow子群的。由于我们的双射与有理数上的绝对伽罗瓦群的作用可换，我们得出结论，特征标对应的值域是相同的。我们用它来回答R.天啊
Letbe an odd prime power,, and letdenote a maximal parabolic subgroup ofwith Levi subgroup. We restrict the odd-degree irreducible characters oftoto discover a natural correspondence of characters, both forand. A similar result is established for certain finite groups with self-normalizing Sylow-subgroups. Next, we construct a canonical bijection between the odd-degree irreducible characters of,orwithodd, and those of, whereis a Sylow-subgroup of. Since our bijections commute with the action of the absolute Galois group over the rationals, we conclude that the fields of values of character correspondents are the same. We use this to answer some questions of R. Gow.