Geodesic
Functoriality Properties of the Dual Group
Documenta mathematica, Tome 24 (2019), pp. 47-64.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Let $G$ be a connected reductive group. Previously, it was shown that for any $G$-variety $X$ one can define the dual group $G^\vee_X$ which admits a natural homomorphism with finite kernel to the Langlands dual group $G^\vee$ of $G$. Here, we prove that the dual group is functorial in the following sense: if there is a dominant $G$-morphism $X\to Y$ or an injective $G$-morphism $Y\to X$ then there is a unique homomorphism with finite kernel $G^\vee_Y\to G^\vee_X$ which is compatible with the homomorphisms to $G^\vee$.
Classification : 17B22, 14L30, 11F70
Keywords: spherical variety, Langlands dual group, root system, algebraic group, reductive group 
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     author = {Knop, Friedrich},
     title = {Functoriality {Properties} of the {Dual} {Group}},
     journal = {Documenta mathematica},
     pages = {47--64},
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     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a61/}
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Knop, Friedrich. Functoriality Properties of the Dual Group. Documenta mathematica, Tome 24 (2019), pp. 47-64. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a61/