Logarithmic Frobenius structures and Coxeter discriminants

Feigin, M. and Veselov, A.P. (2007) Logarithmic Frobenius structures and Coxeter discriminants. Advances in Mathematics, 212(1), pp. 143-162. (doi: 10.1016/j.aim.2006.08.010)

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Publisher's URL: http://dx.doi.org/10.1016/j.aim.2006.08.010


We consider a class of solutions of the WDVV equation related to the special systems of covectors (called V-systems) and show that the corresponding logarithmic Frobenius structures can be naturally restricted to any intersection of the corresponding hyperplanes. For the Coxeter arrangements the corresponding structures are shown to be almost dual in Dubrovin's sense to the Frobenius structures on the strata in the discriminants discussed by Strachan. For the classical Coxeter root systems this leads to the families of V-systems from the earlier work by Chalykh and Veselov. For the exceptional Coxeter root systems we give the complete list of the corresponding V-systems. We present also some new families of V-systems, which cannot be obtained in such a way from the Coxeter root systems.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Feigin, Professor Misha
Authors: Feigin, M., and Veselov, A.P.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Advances in Mathematics
ISSN (Online):1090-2082
Published Online:28 November 2006

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