Kazhdan-Lusztig-Stanley多项式的代数几何

IF 1.3 Q1 MATHEMATICS EMS Surveys in Mathematical Sciences Pub Date : 2017-12-04 DOI:10.4171/EMSS/28
N. Proudfoot
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引用次数: 19

摘要

Kazhdan-Lusztig- stanley多项式是对Coxeter群的Kazhdan-Lusztig多项式的组合推广,Coxeter群包括多体的g多项式和拟阵的Kazhdan-Lusztig多项式。在Weyl群、有理多面体和可实现的拟阵的情况下,我们可以在旗变、环变或互反平面上计算有限域上的点,以获得这些多项式的上同调解释。我们调查了这些结果,并将它们统一在一个单一的几何框架下。
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The algebraic geometry of Kazhdan–Lusztig–Stanley polynomials
Kazhdan-Lusztig-Stanley polynomials are a combinatorial generalization of Kazhdan-Lusztig polynomials of for Coxeter groups that include g-polynomials of polytopes and Kazhdan-Lusztig polynomials of matroids. In the cases of Weyl groups, rational polytopes, and realizable matroids, one can count points over finite fields on flag varieties, toric varieties, or reciprocal planes to obtain cohomological interpretations of these polynomials. We survey these results and unite them under a single geometric framework.
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CiteScore
2.30
自引率
0.00%
发文量
4
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