Galois-equivariant McKay bijections for primes dividing q-1

2020/07/30 by A. A. Schaeffer Fry, Fry, A. A. Schaeffer · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2007.15575

openalex publication_date 2020/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• The Isaacs--Navarro Galois conjecture
• Towards the inductive McKay--Navarro Condition for groups of Lie type

Related

• The inductive McKay-Navarro conditions for the prime 2 and some groups of Lie type
• Towards the inductive McKay--Navarro Condition for groups of Lie type
• On equivariant bijections relative to the defining characteristic
• The McKay--Navarro conjecture for the prime 2
• The inductive McKay--Navarro condition for the Suzuki and Ree groups