Legendre transforms for type $A_{n}$ and $B_{n}$ $\vee$-systems

Misha Feigin; Leo Kaminski; Ian A. B. Strachan

doi:10.1088/1751-8121/ad8cb3

paper

Legendre transforms for type $A_{n}$ and $B_{n}$ $\lor$ -systems

arXiv:2407.20349 · doi:10.1088/1751-8121/ad8cb3

Abstract

The Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations have a rich structure related to the theory of Frobenius manifolds, with many known families of solutions. A Legendre transformation is a symmetry of the WDVV equations, introduced by Dubrovin. We explicitly compute the results of a Legendre transformation applied to $A_{n}$ - and $B_{n}$ -type multi-parameter rational solutions, relating them to known and new trigonometric solutions.

28 pages

Legendre transforms for type An​ and Bn​ ∨-systems

Abstract

Legendre transforms for type $A_{n}$ and $B_{n}$ $\lor$ -systems