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Twisted GL\(_n\) loop group orbit and solutions of the WDVV equations. (English) Zbl 0991.37042

The author considers a twisted \(\text{GL}_n\) loop group and its homogeneous space \(\text{gr}^{(2)}\) related to the infinite-dimensional Sato Grassmannian. It is shown that \(\tau\)-functions \(\tau_W\) associated to points \(W\in\text{gr}^{(2)}\) lead to solutions of the Darboux-Egoroff system as well as WDVV equations.

MSC:

37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
81T45 Topological field theories in quantum mechanics
53D45 Gromov-Witten invariants, quantum cohomology, Frobenius manifolds
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