van de Leur, Johan Twisted GL\(_n\) loop group orbit and solutions of the WDVV equations. (English) Zbl 0991.37042 Int. Math. Res. Not. 2001, No. 11, 551-573 (2001). 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. Reviewer: Igor Potemine (Toulouse) Cited in 8 Documents 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 Keywords:Darboux-Egoroff system; multicomponent KP hierarchy; twisted loop group orbits; WDVV equations PDFBibTeX XMLCite \textit{J. van de Leur}, Int. Math. Res. Not. 2001, No. 11, 551--573 (2001; Zbl 0991.37042) Full Text: DOI arXiv