铺装拟阵的等变Kazhdan-Lusztig理论

Q3 Mathematics Algebraic Combinatorics Pub Date : 2022-02-14 DOI:10.5802/alco.281

Trevor K. Karn, George D. Nasr, N. Proudfoot, Lorenzo Vecchi

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引用次数: 2

摘要

研究了拟阵的等变Kazhdan-Lusztig多项式、等变逆Kazhdan-Lusztig多项式和等变z多项式在应力超平面集合松弛作用下的变化方式。这允许我们计算任意铺装拟阵的多项式，我们在许多例子中都这样做，包括与承认Mathieu群作用的Steiner系统相关的各种拟阵。

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Equivariant Kazhdan–Lusztig theory of paving matroids

We study the way in which equivariant Kazhdan-Lusztig polynomials, equivariant inverse Kazhdan-Lusztig polynomials, and equivariant Z-polynomials of matroids change under the operation of relaxation of a collection of stressed hyperplanes. This allows us to compute these polynomials for arbitrary paving matroids, which we do in a number of examples, including various matroids associated with Steiner systems that admit actions of Mathieu groups.

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