相关论文: On the inductive McKay--Navarro condition for $\ma…

We gather tools for proving the inductive McKay--Navarro (or Galois--McKay) condition for groups of Lie type and odd primes. We use this to establish a bijection in the case of quasisimple groups of Lie type A satisfying the equivariance…

For a prime $\ell$, the McKay conjecture suggests a bijection between the set of irreducible characters of a finite group with $\ell'$-degree and the corresponding set for the normalizer of a Sylow $\ell$- subgroup. Navarro's refinement…

We verify the inductive McKay--Navarro condition for the Suzuki and Ree groups for all primes as well as for $p=3$ and the groups $PSL_3(q)$ with $q \equiv 4,7$ mod $9$, $PSU_3(q) $ with $q \equiv 2,5$ mod $9$, and $G_2(q)$ with $q=2,4,5,7$…

We complete the proof of the McKay--Navarro conjecture (also known as the Galois--McKay conjecture) for the prime 2, by completing the proof of the inductive McKay--Navarro conditions introduced by Navarro--Sp\"ath--Vallejo in this…

The McKay--Navarro conjecture is a refinement of the McKay conjecture that additionally takes the action of some Galois automorphisms into account. We verify the inductive McKay--Navarro condition in the defining characteristic for the…

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…

We establish the inductive McKay condition introduced by Isaacs-Malle-Navarro \cite{IMN} for finite simple groups of Lie types $\tB_l$ ($l\geq 2$), $\tE_6$, $^2\tE_6$ and $\tE_7$, thus leaving open only the types $\tD$ and $^2\tD$. We bring…

We verify the inductive McKay condition for simple groups of Lie type C, namely finite projective symplectic groups. This contributes to the program of a complete proof of the McKay conjecture for all finite groups via the reduction theorem…

As a step to establish the McKay conjecture on character degrees of finite groups, we verify the inductive McKay condition introduced by Isaacs-Malle-Navarro for simple groups of Lie type $A_{n-1}$, split or twisted. Key to the proofs is…

In this paper we consider the inductive Alperin--McKay condition for isolated blocks of groups of Lie type $B$ and $C$. This finishes the verification of the inductive condition for groups of this type.

In this paper, we prove that a refinement of the Alperin-McKay Conjecture for $p$-blocks of finite groups, formulated by I. M. Isaacs and G. Navarro in 2002, holds for all covering groups of the symmetric and alternating groups, whenever…

We reformulate the inductive McKay condition, from Isaacs-Malle-Navarro, and apply the new criterion to simple groups of Lie type, when the prime is the defining characteristic p. Thereby we make use of a recent result of Maslowski. This…

In this paper we consider the inductive Alperin-McKay condition for quasi-isolated 2-blocks of exceptional groups of Lie type. Thereby, we complete the proof of the Alperin-McKay conjecture for the prime 2.

We check McKay conjecture on character degrees for the case of symplectic groups over the field with two elements Sp(2n,2) and the prime 2. Then we check the inductive McKay condition (Isaacs-Malle-Navarro 2007) for Sp(4,2^m) and all…

By the reduction theorems of Navarro--Tiep and Sp\"ath, a way to prove the Alperin weight conjecture and its blockwise version is to verify the co-called inductive Alperin weight condition and inductive blockwise Alperin weight condition…

We complete the proof of the inductive Feit condition and the inductive Galois-McKay condition for the simple groups $\operatorname{PSL}_2(q)$. We also prove that the Suzuki groups $^{2}B_2(2^{2n+1})$ satisfy the inductive Feit condition.

The inductive blockwise Alperin weight condition is a system of conditions whose verification for all non-abelian finite simple groups would imply the blockwise Alperin weight conjecture. We establish this condition for the groups $G_2(q)$,…

Recently Navarro proposed a strengthening of the unsolved McKay conjecture using Galois automorphisms. We prove that the Navarro conjecture holds for the alternating groups when the prime p is odd.

This paper is a contribution to the general program introduced by Isaacs, Malle and Navarro to prove the McKay conjecture in the representation theory of finite groups. We develop new methods for dealing with simple groups of Lie type in…

The so-called inductive McKay condition on finite simple groups, due to Isaacs-Malle-Navarro (2007), has been recently reformulated by Sp\"ath. We show that this reformulation applies to the reduction theorem for Alperin's weight…