Mirror symmetry for extended affine Weyl groups
| Autor: | Brini, Andrea, van Gemst, Karoline |
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| Rok vydání: | 2021 |
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| Zdroj: | Journal de l'\'Ecole polytechnique -- Math\'ematiques, Volume 9 (2022), pp. 907-957 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.5802/jep.197 |
| Popis: | We give a uniform, Lie-theoretic mirror symmetry construction for the Frobenius manifolds defined by Dubrovin-Zhang in arXiv:hep-th/9611200 on the orbit spaces of extended affine Weyl groups, including exceptional Dynkin types. The B-model mirror is given by a one-dimensional Landau-Ginzburg superpotential constructed from a suitable degeneration of the family of spectral curves of the affine relativistic Toda chain for the corresponding affine Poisson--Lie group. As applications of our mirror theorem we give closed-form expressions for the flat coordinates of the Saito metric and the Frobenius prepotentials in all Dynkin types, compute the topological degree of the Lyashko-Looijenga mapping for certain higher genus Hurwitz space strata, and construct hydrodynamic bihamiltonian hierarchies (in both Lax-Sato and Hamiltonian form) that are root-theoretic generalisations of the long-wave limit of the extended Toda hierarchy. Comment: 44 pages; v2: 54 pages, version accepted for publication on J. Ecol. Polytech (Math). A typo in Corollary 5.2 and Table 3 is fixed compared to the published version |
| Databáze: | arXiv |
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