论文标题
符号矩阵和量子哈密顿还原的几乎通勤方案
Almost commuting scheme of symplectic matrices and quantum Hamiltonian reduction
论文作者
论文摘要
Losev介绍了几乎通勤元素的$ x $（即，$ \ mathfrak {g} = \ mathfrak {sp}（v）$的几乎通勤元素（即，通勤至最高元素的元素）$ x $，用于符号矢量空间$ v $，并讨论了其代数字体的属性。我们构造了$ x $的拉格朗日亚cheme $ x^{nil} $，并表明它是dimension $ \ text {dim}（\ mathfrak {g}）+\ frac {1} {1} {2} {2} \ text {dim}（dim}（v）$的完整交点。 我们还研究了代数$ \ MATHCAL {D}（\ Mathfrak {g}）的量子减少差异操作员在Lie代数$ \ Mathfrak {G} $上与Weyl代数相对于某些符号群的作用，并显示了某些spra sphra sphra sphra sphra sphra sphra sphra sphra sphra sphra sphra sphra，nie代数的运算符在lie代数$ \ mathfrak {g} $上$ c $的Cherednik代数。
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 $C$.
