Diagonal invariants and genus-zero Hurwitz Frobenius manifolds
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908751525576704 |
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| author | Proserpio, Alessandro Strachan, Ian A. B. |
| author_facet | Proserpio, Alessandro Strachan, Ian A. B. |
| contents | The Frobenius manifold structure on the space of rational functions with multiple simple poles is constructed. In particular, the dependence of the Saito-flat coordinates on the flat coordinates of the intersection form is studied. While some of the individual flat coordinates are complicated rational functions, they appear in the prepotential in certain combinations known as diagonal invariants, which turn out to be polynomial. Two classes are studied in more detail. These are generalisations of the Coxeter and extended-affine-Weyl orbits space for the group $W=W(A_\ell)\,.$ An invariant theory is also developed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_05165 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diagonal invariants and genus-zero Hurwitz Frobenius manifolds Proserpio, Alessandro Strachan, Ian A. B. Mathematical Physics Exactly Solvable and Integrable Systems 53D45 (Primary), 20F55, 37K25 (Secondary) The Frobenius manifold structure on the space of rational functions with multiple simple poles is constructed. In particular, the dependence of the Saito-flat coordinates on the flat coordinates of the intersection form is studied. While some of the individual flat coordinates are complicated rational functions, they appear in the prepotential in certain combinations known as diagonal invariants, which turn out to be polynomial. Two classes are studied in more detail. These are generalisations of the Coxeter and extended-affine-Weyl orbits space for the group $W=W(A_\ell)\,.$ An invariant theory is also developed. |
| title | Diagonal invariants and genus-zero Hurwitz Frobenius manifolds |
| topic | Mathematical Physics Exactly Solvable and Integrable Systems 53D45 (Primary), 20F55, 37K25 (Secondary) |
| url | https://arxiv.org/abs/2412.05165 |