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arXiv · 2506.11569

From Adler-Gelfand-Dickey Brackets to Logarithmic Dubrovin-Frobenius manifolds

Yassir Dinar
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Abstract

We construct a new local Poisson bracket compatible with the second unconstrained Adler-Gelfand-Dickey bracket. The resulting bihamiltonian structure admits a dispersionless limit and the leading term defines a logarithmic Dubrovin-Frobenius manifold. Furthermore, we show that this Dubrovin-Frobenius manifold can be constructed on the orbits space of the standard representation of the permutation group.

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Yassir Dinar. 2025-06-13. From Adler-Gelfand-Dickey Brackets to Logarithmic Dubrovin-Frobenius manifolds. https://arxiv.org/abs/2506.11569

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