论文标题
抛物线的lusztig品种和色度对称功能
Parabolic Lusztig varieties and chromatic symmetric functions
论文作者
论文摘要
Hecke代数的kazhdan- lusztig元素的字符超过$ s_n $（尤其是，无差异图的色度对称函数）在（交集）共同体的某些子视图品种的（交集）共同体中完全编码。考虑到某个部分标志品种的健忘地图，分解定理告诉我们，在某些部分标志品种的局部局部系统中，这种同胞分裂为具有系数的相交共同体学组的总和。我们证明这些本地系统对应于$ s_n $的子组的表示。 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.我们还发现了部分旗品品种的某些同源群的特征与Hecke代数的Grojnowski-Haiman混合基础之间的联系。
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.
