Inverse Hamiltonian reduction in type A and generalized slices in the affine Grassmannian
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918130076352512 |
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| author | Butson, Dylan Nair, Sujay |
| author_facet | Butson, Dylan Nair, Sujay |
| contents | We give a geometric proof of inverse Hamiltonian reduction for all finite W-algebras in type $A$, a certain embedding of the finite W-algebra corresponding to an arbitrary nilpotent in $\mathfrak{gl}_N$ into that corresponding to a larger nilpotent with respect to the closure order on orbits, tensored with an auxiliary algebra of differential operators. We first prove a classical analogue for equivariant Slodowy slices using multiplication maps on generalized slices in the affine Grassmannian, then deduce the result for equivariant finite W-algebras by Fedosov quantization. This implies the statement for finite W-algebras, as well as Kostant-Whittaker reductions of arbitrary algebras in the category of Harish Chandra bimodules, including quantizations of Moore-Tachikawa varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19882 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inverse Hamiltonian reduction in type A and generalized slices in the affine Grassmannian Butson, Dylan Nair, Sujay Representation Theory High Energy Physics - Theory Algebraic Geometry Quantum Algebra We give a geometric proof of inverse Hamiltonian reduction for all finite W-algebras in type $A$, a certain embedding of the finite W-algebra corresponding to an arbitrary nilpotent in $\mathfrak{gl}_N$ into that corresponding to a larger nilpotent with respect to the closure order on orbits, tensored with an auxiliary algebra of differential operators. We first prove a classical analogue for equivariant Slodowy slices using multiplication maps on generalized slices in the affine Grassmannian, then deduce the result for equivariant finite W-algebras by Fedosov quantization. This implies the statement for finite W-algebras, as well as Kostant-Whittaker reductions of arbitrary algebras in the category of Harish Chandra bimodules, including quantizations of Moore-Tachikawa varieties. |
| title | Inverse Hamiltonian reduction in type A and generalized slices in the affine Grassmannian |
| topic | Representation Theory High Energy Physics - Theory Algebraic Geometry Quantum Algebra |
| url | https://arxiv.org/abs/2503.19882 |