摘要翻译:
计算Khovanov和Rozansky的三次链环同调理论的一个重要步骤是确定SL(n)的Soergel双模的Hochschild同调。对于任何简单群G,我们给出了这种Hochschild同调的几何模型,作为G中B×B-轨道闭包的等变交同调。我们证明了在类型a中,这些轨道闭包对于共轭T-作用是等变形式的。利用这一事实证明了在相应的轨道闭包是光滑的情况下,这个Hochschild同调是生成元上多项式环上的外代数,它的次由轨道闭包的几何显式决定,并描述了它的Hilbert级数,证明了Jacob Rasmussen的一个猜想。
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英文标题:
《A geometric model for Hochschild homology of Soergel bimodules》
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作者:
Ben Webster, Geordie Williamson
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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: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:
An important step in the calculation of the triply graded link homology theory of Khovanov and Rozansky is the determination of the Hochschild homology of Soergel bimodules for SL(n). We present a geometric model for this Hochschild homology for any simple group G, as equivariant intersection homology of B x B-orbit closures in G. We show that, in type A these orbit closures are equivariantly formal for the conjugation T-action. We use this fact to show that in the case where the corresponding orbit closure is smooth, this Hochschild homology is an exterior algebra over a polynomial ring on generators whose degree is explicitly determined by the geometry of the orbit closure, and describe its Hilbert series, proving a conjecture of Jacob Rasmussen.
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PDF链接:
https://arxiv.org/pdf/0707.2003