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arXiv · 1904.04586

Green functions and Glauberman degree-divisibility

Meinolf Geck
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Abstract

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.

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Meinolf Geck. 2019-04-09. Green functions and Glauberman degree-divisibility. https://arxiv.org/abs/1904.04586

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