Parabolic Lusztig varieties and chromatic symmetric functions
Parabolic Lusztig varieties and chromatic symmetric functions
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抛物线 Lusztig 簇和色对称函数
DOI：
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Antonio Nigro
中科院分区：
文献类型：
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作者：
Alex Abreu;Antonio Nigro
. Sn上的Hecke代数的Kazhdan-Lusztig元的特征（特别是异数图的色对称函数）完全编码在Hecke簇的某些子簇的（交）上同调中.分解定理告诉我们，对于到某个部分代数簇的遗忘映射，这个上同调分裂为一个交上同调群的和，这些交上同调群的系数在该部分代数簇的某些局部子簇系中。我们证明，这些局部系统对应于表示的子群Sn。这种表示的一个明确的特征将提供一个计算这种特征标/色对称函数的递归公式，从而解决Haiman关于Kazhdan-Lusztig元素的单项特征标的正性猜想和Stanley-Stembridge关于无差图的色对称函数的正性猜想.我们还发现了部分格簇的子簇的某些同调群的特征与Hecke代数的Grojnowski-Haiman杂交基之间的联系。
. The characters of Kazhdan–Lusztig elements of the Hecke algebra over S n (and in particular, the chromatic symmetric function of indifference graphs) are completely encoded in the (intersection) cohomology of certain subvarieties of the flag variety. Considering the forgetful map to some partial flag variety, the decomposition theorem tells us that this cohomology splits as a sum of intersection cohomology groups with coefficients in some local systems of subvarieties of the partial flag variety. We prove that these local systems correspond to representations of subgroups of S n . An explicit characterization of such representations would provide a recursive formula for the computation of such characters/chromatic symmetric functions, which could settle Haiman’s conjecture about the positivity of the monomial characters of Kazhdan–Lusztig elements and Stanley–Stembridge conjecture about e -positivity of chromatic symmetric function of indifference graphs. We also find a connection between the character of certain homology groups of subvarieties of the partial flag varieties and the Grojnowski–Haiman hybrid basis of the Hecke algebra.
正则半单Hessenberg簇等变上同调环中的排列基
DOI：
10.1007/s44007-021-00016-5
发表时间：
2022
期刊：
La Matematica
影响因子：
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作者：
Harada, Megumi;Precup, Martha;Tymoczko, Julianna
通讯作者：
Tymoczko, Julianna