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Green functions and Glauberman degree-divisibility. (English) Zbl 07239274
Summary: The Glauberman correspondence is a fundamental bijection in the character theory of finite groups. In 1994, Hartley and Turull established a degree-divisibility property for characters related by that correspondence, subject to a congruence condition which should hold for the Green functions of finite groups of Lie type, as defined by Deligne and Lusztig. Here, we present a general argument for completing the proof of that congruence condition. Consequently, the degree-divisibility property holds in complete generality.
##### MSC:
 20C33 Representations of finite groups of Lie type 20C15 Ordinary representations and characters 20G40 Linear algebraic groups over finite fields
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##### References:
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