A Pieri type formula for motivic Chern classes of Schubert cells in Grassmannians
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929236214808576 |
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| author | Fan, Neil J. Y. Guo, Peter L. Su, Changjian Xiong, Rui |
| author_facet | Fan, Neil J. Y. Guo, Peter L. Su, Changjian Xiong, Rui |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04500 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Pieri type formula for motivic Chern classes of Schubert cells in Grassmannians Fan, Neil J. Y. Guo, Peter L. Su, Changjian Xiong, Rui Combinatorics Algebraic Geometry Representation Theory 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. |
| title | A Pieri type formula for motivic Chern classes of Schubert cells in Grassmannians |
| topic | Combinatorics Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2402.04500 |