Trigonometric V-systems and solutions of WDVV equations

Alkadhem, M. and Feigin, M. (2020) Trigonometric V-systems and solutions of WDVV equations. Journal of Physics A: Mathematical and Theoretical, 54, 024002. (doi: 10.1088/1751-8121/abccf8)

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 bigvee-system, and we show that its subsystems are also trigonometric bigvee-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.

• Item Type: Articles
• Additional Information: The work of M.A was funded by Imam Abdulrahman Bin Faisal University, Kingdom of Saudi Arabia, Dammam.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Alkadhem, Maali Alawi J and Feigin, Professor Misha
• Authors: Alkadhem, M., and Feigin, M.
• College/School: College of Science and Engineering; College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Physics A: Mathematical and Theoretical
• Publisher: IOP Publishing
• ISSN: 1751-8113
• ISSN (Online): 1751-8121
• Copyright Holders: Copyright © 2020 The Author(s)
• First Published: First published in Journal of Physics A: Mathematical and Theoretical 54:024002
• Publisher Policy: Reproduced under a Creative Commons license