The dual group of a spherical variety
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- by F. Knop and B. Schalke
- Trans. Moscow Math. Soc. 2017, 187-216
- DOI: https://doi.org/10.1090/mosc/270
- Published electronically: December 1, 2017
Abstract:
Let $X$ be a spherical variety for a connected reductive group $G$. Work of Gaitsgory and Nadler strongly suggests that the Langlands dual group $G^\vee$ of $G$ has a subgroup whose Weyl group is the little Weyl group of $X$. Sakellaridis and Venkatesh defined a refined dual group $G^\vee _X$ and verified in many cases that there exists an isogeny $\varphi$ from $G^\vee _X$ to $G^\vee$. In this paper, we establish the existence of $\varphi$ in full generality. Our approach is purely combinatorial and works (despite the title) for arbitrary $G$-varieties.References
Bibliographic Information
- F. Knop
- Affiliation: Department of Mathematics, FAU Erlangen-Nürnberg, Germany
- MR Author ID: 103390
- ORCID: 0000-0002-4908-4060
- Email: friedrich.knop@fau.de
- B. Schalke
- Affiliation: Department of Mathematics, FAU Erlangen-Nürnberg, Germany
- Email: schalke@math.fau.de
- Published electronically: December 1, 2017
- © Copyright 2017 F. Knop, B. Schalke
- Journal: Trans. Moscow Math. Soc. 2017, 187-216
- MSC (2010): Primary 17B22, 14L30, 11F70
- DOI: https://doi.org/10.1090/mosc/270
- MathSciNet review: 3738085
Dedicated: To Ernest B. Vinberg on the occasion of his 80th birthday