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• W2034275805 abstract "We give a classification of irreducible characters of finite groups of Lie type of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=p prime> <mml:semantics> <mml:msup> <mml:mi>p</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:annotation encoding=application/x-tex>p’</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-degree, where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=p> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=application/x-tex>p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is any prime different from the defining characteristic, in terms of local data. More precisely, we give a classification in terms of data related to the normalizer of a suitable Levi subgroup, which in many cases coincides with the normalizer of a Sylow <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=p> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=application/x-tex>p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-subgroup. The McKay conjecture asserts that there exists a bijection between characters of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=p prime> <mml:semantics> <mml:msup> <mml:mi>p</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:annotation encoding=application/x-tex>p’</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-degree of a group and of the normalizer of a Sylow <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=p> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=application/x-tex>p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-subgroup. We hope that our result will constitute a major step towards a proof of this conjecture for groups of Lie type, and, in conjunction with a recent reduction result of Isaacs, Malle and Navarro, for arbitrary finite groups." @default.
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• W2034275805 title "Height 0 characters of finite groups of Lie type" @default.
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