Covexillary Schubert varieties and Kazhdan–Lusztig polynomials

Minyoung Jeon
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Abstract

We establish combinatorial and inductive formulas for Kazhdan–Lusztig polynomials associated to covexillary elements in classical types, extending results of Boe, Lascoux–Schützenberger, Sankaran–Vanchinathan, and Zelevinsky for Grassmannians of classical types. The proof uses intersection cohomology theory and the isomorphism of Kazhdan–Lusztig varieties from Anderson–Ikeda–Jeon–Kawago.
康维希尔舒伯特变项和卡兹丹-卢兹蒂格多项式
我们建立了与经典类型中的觊觎元素相关的卡兹丹-卢兹提格多项式的组合和归纳公式,扩展了博伊、拉斯科-舒岑贝格、桑卡兰-万钦那坦和泽列文斯基对经典类型格拉斯曼的研究成果。证明使用了交点同调理论和安德森-池田-郑-川子的卡兹丹-卢兹提格变体同构。
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