Poincaré polynomials of generic torus orbit closures in Schubert varieties

Eunjeong Lee, M. Masuda, Seonjeong Park, Jongbaek Song
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引用次数: 5

Abstract

The closure of a generic torus orbit in the flag variety G / B G/B of type  A A is known to be a permutohedral variety, and its Poincaré polynomial agrees with the Eulerian polynomial. In this paper, we study the Poincaré polynomial of a generic torus orbit closure in a Schubert variety in  G / B G/B . When the generic torus orbit closure in a Schubert variety is smooth, its Poincaré polynomial is known to agree with a certain generalization of the Eulerian polynomial. We extend this result to an arbitrary generic torus orbit closure which is not necessarily smooth.
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Schubert变种中一般环面轨道闭包的poincar多项式
已知a型旗型G/B G/B中一般环面轨道的闭包为复面体型,其庞加莱格多项式符合欧拉多项式。本文研究了G/B G/B中舒伯特变中一般环面轨道闭包的poincar多项式。当舒伯特变元中的一般环面轨道闭包是光滑的时,已知其庞卡罗莱多项式符合欧拉多项式的某种推广。我们将这个结果推广到一个不一定光滑的任意一般环面轨道闭包。
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