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International Mathematics Research Notices (2007) Vol. 2007 : article ID rnm020, 24 pages, doi:10.1093/imrn/rnm020 published on May 24, 2007
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Copyright © The Author 2007. Published by Oxford University Press.

Frobenius Manifolds Associated to Bl and Dl, Revisited

Dafeng Zuo

School of Mathematics, Korea Institute for Advanced Study 207-43 Cheongnyangni 2-dong, Dongdaemun-gu Seoul, 130-722 Korea Department of Mathematics, University of Science and Technology, Hefei 230026, P.R.China

Correspondence: Correspondence to be sent to: Dafeng Zuo, School of Mathematics, Korea Institute for Advanced Study 207-43 Cheongnyangni 2-dong, Dongdaemun-gu Seoul, 130-722 Korea. e-mail: dfzuo{at}kias.re.kr, dfzuo{at}ustc.edu.cn

In this paper, we shall construct l Frobenius manifold structures on the orbit spaces of Coxeter groups Bl and Dl. These produce solutions F(t1, ..., tl) of WDVV equations of associativity polynomial in t1, t2, ..., tl, Formula. We also show that F(t1, ..., tl) coincides (up to equivalence) with the Frobenius structure obtained by M.Bertola in [6, 7]. Finally, by using a particular water-bag reduction of the KP hierarchy, we discuss the deformation of solutions to WDVV equations associated to Bl and Dl.

Communicated by Igor Krichever


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