The dual group of a spherical variety - Knop, Friedrich; Schalke, Barbara (Transactions of the Moscow Mathematical Society, 2017)
Let X be a spherical variety for a connected reductive group G. Work of Gaitsgory-Nadler strongly suggests that the Langlands dual group Gv of G has a subgroup whose Weyl group is the little Weyl group of X. Sakellaridis-Venkatesh defined a refined dual group GvX and verified in many cases that there exists an isogeny φ from GvX to Gv. In this paper, we establish the existence of φ in full generality. Our approach is purely combinatorial and works (despite the title) for arbitrary G-varieties.
Keywords: spherical variety; dual group; Langlands program