Related papers: Equivariant character correspondences and inductiv…

Let $G$ be an arbitrary finite group. The McKay conjecture asserts that $G$ and the normaliser $N_G (P)$ of a Sylow $p$-subgroup $P$ in $G$ have the same number of characters of degree not divisible by $p$ (that is, of $p'$-degree). We…

The Alperin-McKay conjecture relates height zero characters of an $\ell$-block with the ones of its Brauer correspondent. This conjecture has been reduced to the so-called inductive Alperin-McKay conditions about quasi-simple groups by the…

In [7], G. Navarro proposed a refinement of the McKay conjecture involving a special class of Galois automorphisms. In [6] this new conjecture was verified by the author for the alternating groups A(n) when p=2. In this note the Navarro…

This article is concerned with the relative McKay conjecture for finite reductive groups. Let G be a connected reductive group defined over the finite field F_q of characteristic p>0 with corresponding Frobenius map F. We prove that if the…

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…

In this paper we prove that a recent condition of Lyons--Mart\'inez--Navarro--Tiep, regarding the field of values of extensions of characters in principal blocks, is satisfied for all finite simple groups, which when combined with their…

The Alperin-McKay conjecture is a longstanding open conjecture in the representation theory of finite groups. Sp\"ath showed that the Alperin-McKay conjecture holds if the so-called inductive Alperin-McKay (iAM) condition holds for all…

We generalize the theory of ordering character triples, developed by Navarro and Sp\"ath, by taking into account the action of Galois automorphisms on characters. This new technique, together with previous results of Ladisch and Turull,…

Recently, Moret\'o and Rizo proposed a conjecture, known as the Picky Conjecture, proposing new character correspondences extending the McKay Conjecture. We prove the Picky Conjecture for all quasi-simple groups of Lie type for non-defining…

Let $N$ be normal subgroup of a finite group $G$, $p$ be a prime, $P$ be a Sylow $p$-subgroup of $G$ and $\theta$ be a $P$-invariant irreducible character of $N$. Suppose that $G/N$ is a $p$-solvable group. In this note we show that,…

Let $P$ be a Sylow $p$-subgroup of a finite $p$-solvable group $G$, where $p$ is a prime. Using a normal $p$-series $\mathcal{N}$ of $G$, we introduce the notion of $(\mathcal{N},p)$-stable characters and prove that $G$ and ${\bf N}_G(P)$…

We verify the inductive McKay--Navarro condition for the groups $\mathsf{B}_2(2^f)$ and $\mathsf{G}_2(3^f)$ and all primes if $f$ is odd. Further, we show that the equivariance part of the inductive condition holds for all integers $f$.

In this paper, we establish the inductive Alperin weight condition for the finite simple groups of Lie type $\mathsf A$, contributing to the program to prove the Alperin weight conjecture by checking the inductive condition for all finite…

In this paper characters of the normaliser of $d$-split Levi subgroups in $\mathrm {SL}_n(q)$ and $\mathrm {SU}_n(q)$ are parametrized with a particular focus on the Clifford theory between the Levi subgroup and its normalizer.These results…

As a sequel to [CS13b], we verify the so-called inductive AM-condition introduced in [Sp12] for simple groups of type A and blocks with maximal defect. This is part of the program set up to verify the Alperin-McKay conjecture through its…

Assume $G$ is a finite symplectic group $\mathrm{Sp}_{2n}(q)$ over a finite field $\mathbb{F}_q$ of odd characteristic. We describe the action of the automorphism group $\mathrm{Aut}(G)$ on the set $\mathrm{Irr}(G)$ of ordinary irreducible…

As a step to establish the blockwise Alperin weight conjecture for all finite groups, we verify the inductive blockwise Alperin weight condition introduced by Navarro--Tiep and Sp\"ath for simple groups of Lie type $\mathsf A$, split or…

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 propose a new refinement of the McKay conjecture and we prove it for symmetric groups.

According to McKay (1980) the irreducible characters of finite subgroups of SU(2) are in a natural 1-1 correspondence with the extended Coxeter-Dynkin graphs of type ADE. We show that the character values themselves can be given by an…