Functoriality Properties of the Dual Group

  • Friedrich Knop

    Department Mathematik, FAU Erlangen-Nürnberg, Cauerstraße 11, D-91058 Erlangen, Germany
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Let GG be a connected reductive group. Previously, it was shown that for any GG-variety XX one can define the dual group GXG^\vee_X which admits a natural homomorphism with finite kernel to the Langlands dual group GG^\vee of GG. Here, we prove that the dual group is functorial in the following sense: if there is a dominant GG-morphism XYX\to Y or an injective GG-morphism YXY\to X then there is a unique homomorphism with finite kernel GYGXG^\vee_Y\to G^\vee_X which is compatible with the homomorphisms to GG^\vee.

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Friedrich Knop, Functoriality Properties of the Dual Group. Doc. Math. 24 (2019), pp. 47–64

DOI 10.4171/DM/674