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摘要翻译：
利用复圈几何研究了微分算子的（扭曲）环对与$\mathfrak{sp}{2n}$的Borel子代数$\mathfrak{sp}_{2n}$相交的最小轨道$\bar O_{\mathrm{min}}$的(Zarisky)闭包的一个特殊不可约分量的奇异性的分解，证明了它们是$\mathfrak{sp}_{2n}$的泛包络代数(UEA)的一个子代数的同态像，该泛包络代数包含决定最小幂零轨道的最大抛物子代数$\mathfrak P$。进一步，利用Weyl代数上的Fourier变换，我们证明了适权射影空间的（扭）环是由同一子代数得到的。最后，从表象理论的角度研究了这个子代数，我们对由上述奇点分解而来的$\mathfrak{sp}{2n}$的UEA发现了新的本原理想，并重新发现了旧的本原理想。
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英文标题：
《Weighted projective spaces and minimal nilpotent orbits》
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作者：
C. A. Rossi
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Rings and Algebras 环与代数
分类描述：Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups
非交换环与代数，非结合代数，泛代数与格论，线性代数，半群
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
We investigate (twisted) rings of differential operators on the resolution of singularities of a particular irreducible component of the (Zarisky) closure of the minimal orbit $\bar O_{\mathrm{min}}$ of $\mathfrak{sp}_{2n}$, intersected with the Borel subalgebra $\mathfrak n_+$ of $\mathfrak{sp}_{2n}$, using toric geometry and show that they are homomorphic images of a subalgebra of the Universal Enveloping Algebra (UEA) of $\mathfrak{sp}_{2n}$, which contains the maximal parabolic subalgebra $\mathfrak p$ determining the minimal nilpotent orbit. Further, using Fourier transforms on Weyl algebras, we show that (twisted) rings of well-suited weighted projective spaces are obtained from the same subalgebra. Finally, investigating this subalgebra from the representation-theoretical point of view, we find new primitive ideals and rediscover old ones for the UEA of $\mathfrak{sp}_{2n}$ coming from the aforementioned resolution of singularities.
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PDF链接：
https://arxiv.org/pdf/0708.1714
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