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arXiv · 2402.04500

A Pieri type formula for motivic Chern classes of Schubert cells in Grassmannians

Neil J. Y. Fan·Peter L. Guo·Changjian Su·Rui Xiong
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Abstract

We prove a Pieri formula for motivic Chern classes of Schubert cells in the equivariant K-theory of Grassmannians, which is described in terms of ribbon operators on partitions. Our approach is to transform the Schubert calculus over Grassmannians to the calculation in a certain affine Hecke algebra. As a consequence, we derive a Pieri formula for Segre motivic classes of Schubert cells in Grassmannians. We apply the Pieri formulas to establish a relation between motivic Chern classes and Segre motivic classes, extending a well-known relation between the classes of structure sheaves and ideal sheaves. As another application, we find a symmetric power series representative for the class of the dualizing sheaf of a Schubert variety.

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Neil J. Y. Fan, Peter L. Guo, Changjian Su, Rui Xiong. 2024-02-07. A Pieri type formula for motivic Chern classes of Schubert cells in Grassmannians. https://arxiv.org/abs/2402.04500

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