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arXiv · 2107.12557

Frobenius manifolds on orbits spaces

Zainab Al-Maamari·Yassir Dinar
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Abstract

The orbits space of an irreducible linear representation of a finite group is a variety whose coordinate ring is the ring of invariant polynomials. Boris Dubrovin proved that the orbits space of the standard reflection representation of an irreducible finite Coxeter group $\mathcal W$ acquires a natural polynomial Frobenius manifold structure. We apply Dubrovin's method on various orbits spaces of linear representations of finite groups. We find some of them has non or several natural Frobenius manifold structures. On the other hand, these Frobenius manifold structures include rational and trivial structures which are not known to be related to the invariant theory of finite groups.

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BibTeXRIS

Zainab Al-Maamari, Yassir Dinar. 2021-07-27. Frobenius manifolds on orbits spaces. https://doi.org/10.1007/s11040-022-09434-5

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