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摘要翻译：
本文给出了一个组合过程（基于Coxeter群的W-图），证明了任意域上系数的低秩复标志簇上的多个交上同调复的性质是由Kazhdan-Lusztig基元给出的。我们的程序利用奇偶轮的存在性和唯一性。特别地，利用Kazhdan-Lusztig基元给出了域上系数为A_n型标志簇的所有交上同调复形的性质。根据Soergel的结果，这意味着Lusztig关于n\le7的SL(n)的部分猜想。我们也给出了我们的技术失败的例子。在Tom Braden的附录中，给出了SL(8)和SO(8)的标志变量上的交上同调复形的例子，这些复形在它们的柄或共柄上有扭转。
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英文标题：
《Modular intersection cohomology complexes on flag varieties》
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作者：
Geordie Williamson
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最新提交年份：
2012
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分类信息：
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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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 present a combinatorial procedure (based on the W-graph of the Coxeter group) which shows that the characters of many intersection cohomology complexes on low rank complex flag varieties with coefficients in an arbitrary field are given by Kazhdan-Lusztig basis elements. Our procedure exploits the existence and uniqueness of parity sheaves. In particular we are able to show that the characters of all intersection cohomology complexes with coefficients in a field on the flag variety of type A_n for n < 7 are given by Kazhdan-Lusztig basis elements. By results of Soergel, this implies a part of Lusztig's conjecture for SL(n) with n \le 7. We also give examples where our techniques fail. In the appendix by Tom Braden examples are given of intersection cohomology complexes on the flag varities for SL(8) and SO(8) which have torsion in their stalks or costalks.
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PDF链接：
https://arxiv.org/pdf/0709.0207
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