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Working paper

Root subgroups on affine spherical varieties

arxiv.org. math. Cornell University, 2021. No. 2012.02088.
Given a connected reductive algebraic group G and a Borel subgroup B⊆G, we study B-normalized one-parameter additive group actions on affine spherical G-varieties. We establish basic properties of such actions and their weights and discuss many examples exhibiting various features. We propose a construction of such actions that generalizes the well-known construction of normalized one-parameter additive group actions on affine toric varieties. Using this construction, for every affine horospherical G-variety X we obtain a complete description of all G-normalized one-parameter additive group actions on X and show that the open G-orbit in X can be connected with every G-stable prime divisor via a suitable choice of a B-normalized one-parameter additive group action. Finally, when G is of semisimple rank 1, we obtain a complete description of all B-normalized one-parameter additive group actions on affine spherical G-varieties having an open orbit of a maximal torus T⊆B.