Lagrangian Subvarieties of Hyperspherical Varieties

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2025年1月22日

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Michael Finkelberg,
Victor Ginzburg,
Roman Travkin

摘要

Given a hyperspherical G-variety 𝒳 we consider the zero moment level Λ_𝒳⊂𝒳 of the action of a Borel subgroup B⊂G. We conjecture that Λ_𝒳 is Lagrangian. For the dual G^∨-variety 𝒳^∨, we conjecture that that there is a bijection between the sets of irreducible components $\operatorname {Irr}\Lambda _{{\mathscr{X}}}$ and $\operatorname {Irr}\Lambda _{{\mathscr{X}}^{\vee }}$ . We check this conjecture for all the hyperspherical equivariant slices, and for all the basic classical Lie superalgebras.