Geodesic
Functoriality Properties of the Dual Group
Documenta mathematica, Tome 24 (2019), pp. 47-64
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Let G be a connected reductive group. Previously, it was shown that for any G-variety X one can define the dual group GX∨​ which admits a natural homomorphism with finite kernel to the Langlands dual group G∨ of G. Here, we prove that the dual group is functorial in the following sense: if there is a dominant G-morphism X→Y or an injective G-morphism Y→X then there is a unique homomorphism with finite kernel GY∨​→GX∨​ which is compatible with the homomorphisms to G∨.
DOI : 10.4171/dm/674
Classification : 11F70, 14L30, 17B22
Mots-clés : reductive group, root system, spherical variety, Langlands dual group, algebraic group 
@article{10_4171_dm_674,
     author = {Friedrich Knop},
     title = {Functoriality {Properties} of the {Dual} {Group}},
     journal = {Documenta mathematica},
     pages = {47--64},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/674},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/674/}
}
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Friedrich Knop. Functoriality Properties of the Dual Group. Documenta mathematica, Tome 24 (2019), pp. 47-64. doi: 10.4171/dm/674

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