Feigin, M. , Valeri, D. and Wright, J. (2024) Flat coordinates of algebraic Frobenius manifolds in small dimensions. Journal of Geometry and Physics, 200, 105151. (doi: 10.1016/j.geomphys.2024.105151)
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Abstract
Orbit spaces of the reflection representation of finite irreducible Coxeter groups provide polynomial Frobenius manifolds. Flat coordinates of the Frobenius 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 Frobenius 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.
| Item Type: | Articles |
|---|---|
| Additional Information: | The work of J.W. was supported by EPSRC (Engineering and Physical Sciences Research Council) via a postgraduate scholarship. D.V. acknowledges the financial support of the project MMNLP (Mathematical Methods in Non Linear Physics) of the INFN, and of the University 2022 grant RM1221815BD9120E. |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Valeri, Dr Daniele and Wright, Johan and Feigin, Professor Misha |
| Authors: | Feigin, M., Valeri, D., and Wright, J. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Journal of Geometry and Physics |
| Publisher: | Elsevier |
| ISSN: | 0393-0440 |
| ISSN (Online): | 1879-1662 |
| Published Online: | 29 February 2024 |
| Copyright Holders: | Copyright © 2024 The Author(s) |
| First Published: | First published in Journal of Geometry and Physics 200:105151 |
| Publisher Policy: | Reproduced under a Creative Commons licence |
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