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- W4313304823 abstract "Losev introduced the scheme $X$ of almost commuting elements (i.e., elements commuting upto a rank one element) of $mathfrak{g}=mathfrak{sp}(V)$ for a symplectic vector space $V$ and discussed its algebro-geometric properties. We construct a Lagrangian subscheme $X^{nil}$ of $X$ and show that it is a complete intersection of dimension $text{dim}(mathfrak{g})+frac{1}{2}text{dim}(V)$ and compute its irreducible components. We also study the quantum Hamiltonian reduction of the algebra $mathcal{D}(mathfrak{g})$ of differential operators on the Lie algebra $mathfrak{g}$ tensored with the Weyl algebra with respect to the action of the symplectic group, and show that it is isomorphic to the spherical subalgebra of a certain rational Cherednik algebra of Type $C$." @default.
- W4313304823 created "2023-01-06" @default.
- W4313304823 creator A5075332473 @default.
- W4313304823 date "2022-12-27" @default.
- W4313304823 modified "2023-09-23" @default.
- W4313304823 title "Almost commuting scheme of symplectic matrices and quantum Hamiltonian reduction" @default.
- W4313304823 doi "https://doi.org/10.48550/arxiv.2212.13436" @default.
- W4313304823 hasPublicationYear "2022" @default.
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