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• W2737474727 abstract "A classical conjecture in the representation theory of finite groups, the McKay conjecture, states that for any finite group and prime number p the number of complex irreducible characters of degree prime to p is equal to the number of complex irreducible characters of degree prime to p of the normalizer of a p-Sylow subgroup. Recently a reduction theorem was proved by Isaacs, Malle and Navarro: If all simple groups are “good”, then the McKay conjecture holds. In this work we are concerned with the problem of goodness for finite groups of Lie type in their defining characteristic. A simple group is called “good” if certain equivariant bijections between the involved character sets exist. We present a structural approach to the construction of such a bijection by utilizing the so-called “Steinberg-Map”. This yields very natural bijections and we prove most of the desired properties." @default.
• W2737474727 created "2017-07-31" @default.
• W2737474727 creator A5037770717 @default.
• W2737474727 date "2010-01-01" @default.
• W2737474727 modified "2023-10-01" @default.
• W2737474727 title "Equivariant character bijections in groups of Lie type" @default.
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• W2737474727 hasPublicationYear "2010" @default.
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