摘要翻译:
设$S$为仿射平面$\c^2$以及适当的$\MathBB T=\c^*$操作。设$\hil{m,m+1}$为关联Hilbert格式。与引用{LQ}平行,我们构造了一个无穷维李代数,它作用于$hil{m,m+1}$的中次等变上同调群的直和$$\wft=\bigoplus_{m=0}^{+\infty}h^{2(m+1)}_{mathbb T}(S^{[m,m+1]})$$。该代数与无穷维Heisenberg代数的环代数有关。此外,我们还研究了$\wft$的三种不同线性基之间的变换。我们的结果应用于$\hil{m,m+1}$的普通上同调的环结构和无穷多变量的对称函数环。
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英文标题:
《Equivariant cohomology of incidence Hilbert schemes and loop algebras》
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作者:
Wei-Ping Li, Zhenbo Qin
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最新提交年份:
2008
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分类信息:
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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一级分类:Mathematics 数学
二级分类:Representation Theory 表象理论
分类描述:Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra
代数和群的线性表示,李理论,结合代数,多重线性代数
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英文摘要:
Let $S$ be the affine plane $\C^2$ together with an appropriate $\mathbb T = \C^*$ action. Let $\hil{m,m+1}$ be the incidence Hilbert scheme. Parallel to \cite{LQ}, we construct an infinite dimensional Lie algebra that acts on the direct sum $$\Wft = \bigoplus_{m=0}^{+\infty}H^{2(m+1)}_{\mathbb T}(S^{[m,m+1]})$$ of the middle-degree equivariant cohomology group of $\hil{m,m+1}$. The algebra is related to the loop algebra of an infinite dimensional Heisenberg algebra. In addition, we study the transformations among three different linear bases of $\Wft$. Our results are applied to the ring structure of the ordinary cohomology of $\hil{m,m+1}$ and to the ring of symmetric functions in infinitely many variables.
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PDF链接:
https://arxiv.org/pdf/0802.1673