Integrable hierarchies associated to infinite families of Frobenius manifolds

2020/07/23 by Alexey Basalaev, Petr Dunin-Barkowski, Sergey Natanzon · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.AG #math.MP

paper · pdf · doi:10.1088/1751-8121/abdd79

published as Journal of Physics A: Mathematical and Theoretical, 2021 · 20 pages

arxiv created 2020/07/23 · arxiv updated 2021/01/22

Abstract

We propose a new construction of an integrable hierarchy associated to any infinite series of Frobenius manifolds satisfying a certain stabilization condition. We study these hierarchies for Frobenius manifolds associated to A_N, D_N and B_N singularities. In the case of A_N Frobenius manifolds our hierarchy turns out to coincide with the KP hierarchy; for B_N Frobenius manifolds it coincides with the BKP hierarchy; and for D_N hierarchy it is a certain reduction of the 2-component BKP hierarchy. As a side product to these results we illustrate the enumerative meaning of certain coefficients of A_N, D_N and B_N Frobenius potentials.

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• BKP and CKP hierarchies via orbifold Saito theory