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arXiv 1210.19082012-10math.ATmath.CO

A Geometric Definition Of Schubert Polynomials and Dual Schubert Polynomials For Classical Lie Groups

Zhao Xu-an, Gao Hongzhu

备注：: This paper has been withdrawn by the author due to a crucial This paper have a vital error in Lemma 2.1. So the definition for Schubert polynomials are not valid for Lie groups of type B,C,D

英文摘要：

In this paper, we first discuss the topological properties of projective Stiefel manifolds, we compute their cohomology rings and classify their cohomology endomorphisms; Then by embedding the flag manifold of a classical Lie group into its corresponding infinite dimensional projective Stiefel manifold(which is homotopic to the product of infinite dimensional complex projective space $\mathbb{C}P^{\infty}$), we define the Schubert polynomials and dual Schubert polynomials. Finally we discuss the property and the computation of these polynomials.

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