TY - RPRT
T1 - Extended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentials
Y1 - 2015
A1 - Boris Dubrovin
A1 - Ian A.B. Strachan
A1 - Youjin Zhang
A1 - Dafeng Zuo
AB - For the root systems of type Bl, Cl and Dl, we generalize the result of [7] by showing the existence of Frobenius manifold structures on the orbit spaces of the extended affine Weyl groups that correspond to any vertex of the Dynkin diagram instead of a particular choice made in [7]. It also depends on certain additional data. We also construct LG superpotentials for these Frobenius manifold structures.
PB - SISSA
UR - http://preprints.sissa.it/handle/1963/35316
U1 - 35625
U2 - Mathematics
U4 - 1
U5 - MAT/07
ER -
TY - JOUR
T1 - On the genus two free energies for semisimple Frobenius manifolds
JF - Russian Journal of Mathematical Physics. Volume 19, Issue 3, September 2012, Pages 273-298
Y1 - 2012
A1 - Boris Dubrovin
A1 - Si-Qi Liu
A1 - Youjin Zhang
AB - We represent the genus two free energy of an arbitrary semisimple Frobenius\\r\\nmanifold as a sum of contributions associated with dual graphs of certain\\r\\nstable algebraic curves of genus two plus the so-called \\\"genus two G-function\\\".\\r\\nConjecturally the genus two G-function vanishes for a series of important\\r\\nexamples of Frobenius manifolds associated with simple singularities as well as\\r\\nfor ${\\\\bf P}^1$-orbifolds with positive Euler characteristics. We explain the\\r\\nreasons for such Conjecture and prove it in certain particular cases.
PB - SISSA
UR - http://hdl.handle.net/1963/6464
N1 - 36 pages, 3 figures
U1 - 6411
U2 - Mathematics
U4 - 1
U5 - MAT/07 FISICA MATEMATICA
ER -
TY - JOUR
T1 - Extended affine Weyl groups and Frobenius manifolds
JF - Compositio Mathematica. Volume 111, Issue 2, 1998, Pages 167-219
Y1 - 1998
A1 - Boris Dubrovin
A1 - Youjin Zhang
PB - Kluwer
UR - http://hdl.handle.net/1963/6486
U1 - 6424
U2 - Mathematics
U4 - 1
U5 - MAT/03 GEOMETRIA
ER -