On the Existence ofB-Root Subgroups on Affine Spherical Varieties

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 normalized by a Borel s...

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Bibliographic Details
Published in:Doklady. Mathematics 2022, Vol.105 (2), p.51-55
Main Authors: Avdeev, R. S., Zhgoon, V. S.
Format: Article
Language:English
Subjects:
Combinatorial analysis
Mathematics
Mathematics and Statistics
Parameters
Subgroups
Online Access:Get full text
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Summary: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 normalized by a Borel subgroup . 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.
ISSN:1064-5624
1531-8362
DOI:10.1134/S1064562422020053