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arXiv · 2007.03818

Generic simplicity of quantum Hamiltonian reductions

Akaki Tikaradze
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Abstract

Let a reductive group $G$ act on a smooth affine complex algebraic variety $X.$ Let $\mathfrak{g}$ be the Lie algebra of $G$ and $μ:T^*(X)\to \mathfrak{g}$ be the moment map. If the moment map is flat, and for a generic character $χ:\mathfrak{g}\to\mathbb{C}$, the action of $G$ on $μ^{-1}(χ)$ is free, then we show that for very generic characters $χ$ the corresponding quantum Hamiltonian reduction of the ring of differential operators $D(X)$ is simple.

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Akaki Tikaradze. 2021-07-12. Generic simplicity of quantum Hamiltonian reductions. https://arxiv.org/abs/2007.03818

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