Orbit spaces of the reflection representation of finite irreducible Coxeter groups provide polynomial Frobenius manifolds. Flat coordinates of the Frobenius manifold metric η are Saito polynomials which are distinguished basic invariants of the Coxeter group. Algebraic Frobenius manifolds are typically related to quasi-Coxeter conjugacy classes in finite Coxeter groups. We find explicit relations between flat coordinates of the metric η and flat coordinates of the intersection form g for most known examples of algebraic Frobenius manifolds up to dimension 4. In all the cases, flat coordinates of the metric η appear to be algebraic functions on the orbit space of the Coxeter group.
Flat coordinates of algebraic Frobenius manifolds in small dimensions / Feigin, Misha; Valeri, Daniele; Wright, Johan. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - (2024). [10.1016/j.geomphys.2024.105151]
Flat coordinates of algebraic Frobenius manifolds in small dimensions
Valeri, Daniele
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2024
Abstract
Orbit spaces of the reflection representation of finite irreducible Coxeter groups provide polynomial Frobenius manifolds. Flat coordinates of the Frobenius manifold metric η are Saito polynomials which are distinguished basic invariants of the Coxeter group. Algebraic Frobenius manifolds are typically related to quasi-Coxeter conjugacy classes in finite Coxeter groups. We find explicit relations between flat coordinates of the metric η and flat coordinates of the intersection form g for most known examples of algebraic Frobenius manifolds up to dimension 4. In all the cases, flat coordinates of the metric η appear to be algebraic functions on the orbit space of the Coxeter group.File | Dimensione | Formato | |
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