Hikita surjectivity for $\mathcal N /// T$
| Autor: | Setiabrata, Linus |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The Hamiltonian reduction $\mathcal N///T$ of the nilpotent cone in $\mathfrak{sl}_n$ 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 $\overline{T^*(G/U)}$ of the cotangent bundle of the base affine space. We construct a surjective map $\mathbb C\left[\overline{T^*(G/U)}^{T\times B/U}\right] \twoheadrightarrow H^*\left(\widetilde{\mathcal N /// T}\right)$ 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. Comment: 19 pages, 5 figures |
| Databáze: | arXiv |
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