Equivariant Chevalley, Giambelli, and Monk Formulae for the Peterson Variety
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866918273902182400 |
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| author | Goldin, Rebecca Singh, Rahul |
| author_facet | Goldin, Rebecca Singh, Rahul |
| contents | We present a formula for the Poincaré dual in the flag manifold of the equivariant fundamental class of any regular nilpotent or regular semisimple Hessenberg variety as a polynomial in terms of certain Chern classes. We then develop a type-independent proof of the Giambelli formula for the Peterson variety, and use this formula to compute the intersection multiplicity of a Peterson variety with an opposite Schubert variety corresponding to a Coxeter word. Finally, we develop an equivariant Chevalley formula for the cap product of a divisor class with a fundamental class, and a dual Monk rule, for the Peterson variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_15663 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Equivariant Chevalley, Giambelli, and Monk Formulae for the Peterson Variety Goldin, Rebecca Singh, Rahul Algebraic Geometry Combinatorics 14N10, 05E14 We present a formula for the Poincaré dual in the flag manifold of the equivariant fundamental class of any regular nilpotent or regular semisimple Hessenberg variety as a polynomial in terms of certain Chern classes. We then develop a type-independent proof of the Giambelli formula for the Peterson variety, and use this formula to compute the intersection multiplicity of a Peterson variety with an opposite Schubert variety corresponding to a Coxeter word. Finally, we develop an equivariant Chevalley formula for the cap product of a divisor class with a fundamental class, and a dual Monk rule, for the Peterson variety. |
| title | Equivariant Chevalley, Giambelli, and Monk Formulae for the Peterson Variety |
| topic | Algebraic Geometry Combinatorics 14N10, 05E14 |
| url | https://arxiv.org/abs/2111.15663 |