Left Demazure-Lusztig operators on equivariant (quantum) cohomology and K theory
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866910888832794624 |
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| author | Mihalcea, Leonardo C. Naruse, Hiroshi Su, Changjian |
| author_facet | Mihalcea, Leonardo C. Naruse, Hiroshi Su, Changjian |
| contents | We study the Demazure-Lusztig operators induced by the left multiplication on partial flag manifolds $G/P$. We prove that they generate the Chern-Schwartz-MacPherson classes of Schubert cells (in equivariant cohomology), respectively their motivic Chern classes (in equivariant K theory), in any partial flag manifold. Along the way we advertise many properties of the left and right divided difference operators in cohomology and K theory, and their actions on Schubert classes. We apply this to construct left divided difference operators in equivariant quantum cohomology, and equivariant quantum K theory, generating Schubert classes, and satisfying a Leibniz rule compatible with the quantum product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_12670 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Left Demazure-Lusztig operators on equivariant (quantum) cohomology and K theory Mihalcea, Leonardo C. Naruse, Hiroshi Su, Changjian Algebraic Geometry Combinatorics Representation Theory Primary 14M15, 20C08, Secondary 14C17, 05E10 We study the Demazure-Lusztig operators induced by the left multiplication on partial flag manifolds $G/P$. We prove that they generate the Chern-Schwartz-MacPherson classes of Schubert cells (in equivariant cohomology), respectively their motivic Chern classes (in equivariant K theory), in any partial flag manifold. Along the way we advertise many properties of the left and right divided difference operators in cohomology and K theory, and their actions on Schubert classes. We apply this to construct left divided difference operators in equivariant quantum cohomology, and equivariant quantum K theory, generating Schubert classes, and satisfying a Leibniz rule compatible with the quantum product. |
| title | Left Demazure-Lusztig operators on equivariant (quantum) cohomology and K theory |
| topic | Algebraic Geometry Combinatorics Representation Theory Primary 14M15, 20C08, Secondary 14C17, 05E10 |
| url | https://arxiv.org/abs/2008.12670 |