Hikita surjectivity for \mathcal N /// T

2024/10/21 by Setiabrata, Linus
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2410.16217

Abstract

The Hamiltonian reduction \mathcal N///T of the nilpotent cone in \mathfraksl_n by the torus of diagonal matrices is a Nakajima quiver variety which admits a symplectic resolution \widetilde\mathcal N///T, and the corresponding BFN Coulomb branch is the affine closure T^*(G/U) of the cotangent bundle of the base affine space. We construct a surjective map \mathbb C[T^*(G/U)^{T× B/U}] \twoheadrightarrow H^*(\widetilde\mathcal N /// T) of graded algebras, which the Hikita conjecture predicts to be an isomorphism. Our map is inherited from a related case of the Hikita conjecture and factors through Kirwan surjectivity for quiver varieties. We conjecture that many other Hikita maps can be inherited from that of a related dual pair.

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