素数除$q-1$的Galois-等变McKay双射
Galois-equivariant McKay bijections for primes dividing $q-1$
摘要：
我们证明了对于大多数Lie型群，Malle和Sp所用的双射aeth在Isaacs-Malle-Navarro的归纳McKay条件的证明中证明了素数2和奇素数整除q - 1也是关于某些Galois自同构等变的。特别地，这表明这些双射是证明Navarro-Sp的候选aeth-Vallejo最近提出的归纳Galois-McKay条件。在此基础上，我们证明了几个李型单群在素数为2时满足McKay-Navarro猜想。
英文摘要：
We prove that for most groups of Lie type, the bijections used by Malle and Spaeth in the proof of Isaacs-Malle-Navarro's inductive McKay conditions for the prime 2 and odd primes dividing q - 1 are also equivariant with respect to certain Galois automorphisms. In particular, this shows that these bijections are candidates for proving Navarro-Spaeth-Vallejo's recently-posited inductive Galois-McKay conditions. On the way, we show that several simple groups of Lie type satisfy the McKay--Navarro conjecture for the prime 2.
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