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arXiv · 2404.19033

Lagrangian subvarieties of hyperspherical varieties related to $G_2$

Nikolay Kononenko
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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.

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Nikolay Kononenko. 2024-04-29. Lagrangian subvarieties of hyperspherical varieties related to $G_2$. https://arxiv.org/abs/2404.19033

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