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Base change and the Mackey formula in Deligne--Lusztig theory
Using ideas of Digne and recent work of Gaitsgory--Rozenblyum--Varshavsky, we show that Lusztig induction commutes with (a minor variant of) the Glauberman correspondence for large prime degree field extensions. This allows one to reduce the Mackey formula in Deligne--Lusztig theory to the case of `
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