Lagrangian subvarieties of hyperspherical varieties related to $G_2$

Nikolay Kononenko

Lagrangian subvarieties of hyperspherical varieties related to $G_2$

Algebraic Geometry 2025-04-30 v2 Representation Theory

Authors: Nikolay Kononenko

Abstract

We consider two $S$ -dual hyperspherical varieties of the group $G_2 \times \text{SL}(2)$ : an equivariant slice for $G_2$ , and the symplectic representation of $G_2 \times \text{SL}_2$ in the odd part of the basic classical Lie superalgebra $\mathfrak{g}(3)$ . For these varieties we check the equality of numbers of irreducible components of their Lagrangian subvarieties (zero levels of the moment maps of Borel subgroups' actions) conjectured in arXiv:2310.19770.

Keywords

Lagrangian subvarieties hyperspherical varieties group $G_2$ moment map Borel subgroups

Cite

@article{arxiv.2404.19033,
  title  = {Lagrangian subvarieties of hyperspherical varieties related to $G_2$},
  author = {Nikolay Kononenko},
  journal= {arXiv preprint arXiv:2404.19033},
  year   = {2025}
}

Comments

v2: some typos fixed; proofs of Lemma 2.2.12, Prop. 3.1.2 corrected

Lagrangian subvarieties of hyperspherical varieties related to $G_2$

Abstract

Keywords

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