Inverse Hamiltonian reduction in type A and generalized slices in the affine Grassmannian

2025/03/25 by Butson, Dylan, Nair, Sujay · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2503.19882

Abstract

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 \mathfrakgl_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.

Cited by

• Characters and fusion rules of boundary W-algebras
• Inverse Hamiltonian reduction for affine W-algebras in type A

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