A special class of solutions to the generalised WDVV equations related to a finite set of covectors is investigated. Some geometric conditions on such a set which guarantee that the corresponding function satisfies WDVV equations are found (boolean OR-conditions). These conditions are satisfied for all root systems and their special deformations discovered in the theory of the Calogero-Moser systems by Chalykh, Feigin and the author. This leads to the new solutions for the generalized WDVV equations.
History
School
Science
Department
Mathematical Sciences
Pages
122961 bytes
Publication date
1999
Notes
This is a pre-print. The definitive version: VESELOV, A.P., 1999. Deformations of the root systems and new solutions to generalised WDVV equations. Physics Letters A, 261(5-6), pp. 297-302, is available at: http://www.sciencedirect.com/science/journal/03759601.