Strengthening the McKay Conjecture to include local fields and local Schur indices
Strengthening the McKay Conjecture to include local fields and local Schur indices
复制标题
强化麦凯猜想以包含局部域和局部 Schur 指数
DOI：
10.1016/j.jalgebra.2005.12.035
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发表时间：
2008
影响因子：
0.9
通讯作者：
A. Turull
中科院分区：
文献类型：
--
作者：
A. Turull
有限群表示理论中的一个中心问题是，给定一个素数p，研究G的表示与G的p-局部子群的表示之间的关系。其中最简单的可能是McKay猜想，它涉及到素数到p的次数的不可约特征标的个数。尽管这个猜想仍然是开放的，但为了理解它，已经提出了一些加强的猜想。最近，Isaacs和Navarro，以及后来的Navarro，提出了有趣的更强的猜想，表明模p的特征标度的同余以及在某些类型的固定Galois自同构下的不变性也可以被考虑在内。我们进一步加强了McKay猜想，并考虑了不可约特征标定义的p-局部域及其p-局部Schur指数。
A central problem in the representation theory of finite groups is, given a prime p, the study of relationships between the representations of G and those of p-local subgroups of G. The simplest of these is perhaps the McKay Conjecture, which concerns the number of irreducible characters of degree prime to p. Even though this conjecture remains open, in an effort to understand it, a number of strengthenings of it have been proposed. Recently, Isaacs and Navarro, and later Navarro, have proposed interesting stronger conjectures indicating that congruences modulo p of the degree of the characters, and the invariance under certain type of fixed Galois automorphism could be taken into account as well. We propose an even further strengthening of McKay's Conjecture which takes into account, in addition, the p-local field of definition of the irreducible characters, as well as their p-local Schur indices.