Trigonometric ∨ -systems and solutions of WDVV equations ^*

Abstract

We consider a class of trigonometric solutions of Witten–Dijkgraaf–Verlinde–Verlinde equations determined by collections of vectors with multiplicities. We show that such solutions can be restricted to special subspaces to produce new solutions of the same type. We find new solutions given by restrictions of root systems, as well as examples which are not of this form. Further, we consider a closely related notion of a trigonometric ∨-system, and we show that its subsystems are also trigonometric ∨-systems. Finally, while reviewing the root system case we determine a version of (generalised) Coxeter number for the exterior square of the reflection representation of a Weyl group.

Integrable physics and its connections with special functions and combinatorics

“…Corrigan and Zambon [12] investigate defects and discontinuities in integrable field theory models, showing that if defects exist between two domains, then discontinuities must exist. While Alkadhem and Feigin [13] look at trigonometric solutions to the WDVV equations. Xingbiao Hu, Pan, Sun, Wang and Zhang [14] investigate numerical algorithms for the modified KdV-sin-Gordon model.…”