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Towards the inductive McKay--Navarro Condition for groups of Lie type

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arxiv 2506.17123 v1 pith:TJNX3ETW submitted 2025-06-20 math.RT math.GR

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keywords conditiongroupsinductivetypemckay--navarrobijectioncasecharacters
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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 properties needed for the condition. We also prove the inductive conditions for the subset of unipotent characters.

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  1. The Isaacs--Navarro Galois conjecture

    math.RT 2025-09 conditional novelty 8.0 of 10

    The Isaacs-Navarro Galois conjecture is proved: for every finite group G and prime l, there is an H0-equivariant bijection between the l'-degree characters of G and those of the normalizer of a Sylow l-subgroup.

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