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On the Existence of B -Root Subgroups on Affine Spherical Varieties

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Abstract

Let X be an irreducible affine algebraic variety that is spherical with respect to an action of a connected reductive group G. In this paper, we provide sufficient conditions, formulated in terms of weight combinatorics, for the existence of one-parameter additive actions on \(X\) normalized by a Borel subgroup \(B \subset G\). As an application, we prove that every G-stable prime divisor in X can be connected with an open G-orbit by means of a suitable B-normalized one-parameter additive action.

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Funding

The research of R.S. Avdeev was supported by the Russian Science Foundation, grant no. 22-41-02019. The research of V.S. Zhgoon was performed within the state assignment for basic scientific research (project no. FNEF-2022-0011) and the HSE University Basic Research Program.

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Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow, Russia

    R. S. Avdeev & V. S. Zhgoon

  2. Scientific Research Institute for System Analysis, Russian Academy of Sciences, Moscow, Russia

    V. S. Zhgoon

Authors
  1. R. S. Avdeev
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  2. V. S. Zhgoon
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Corresponding authors

Correspondence to R. S. Avdeev or V. S. Zhgoon.

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The authors declare that they have no conflicts of interest.

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Translated by I. Ruzanova

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Avdeev, R.S., Zhgoon, V.S. On the Existence of B -Root Subgroups on Affine Spherical Varieties . Dokl. Math. 105, 51–55 (2022). https://doi.org/10.1134/S1064562422020053

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  • DOI: https://doi.org/10.1134/S1064562422020053

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