Lagrangian subvarieties of hyperspherical varieties related to G₂

We consider two S-dual hyperspherical varieties of the group G₂ SL (2): an equivariant slice for G₂, and the symplectic representation of G₂ SL₂ in the odd part of the basic classical Lie superalgebra 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.