Solutions to WDVV from generalized Drinfeld-Sokolov hierarchies
نویسنده
چکیده
The dispersionless limit of generalized Drinfeld-Sokolov hierarchies associated to primitive regular conjugacy class of Weyl group W (g) is discussed. The map from these generalized Drinfeld Sokolov hierarchies to algebraic solutions to WDVV equations has been constructed. Example of g = D4 and [w] = D4(a1) is considered in details and corresponding Frobenius structure is found.
منابع مشابه
Extensions of the matrix Gelfand-Dickey hierarchy from generalized Drinfeld-Sokolov reduction
The p × p matrix version of the r-KdV hierarchy has been recently treated as the reduced system arising in a Drinfeld-Sokolov type Hamiltonian symmetry reduction applied to a Poisson submanifold in the dual of the Lie algebra ĝlpr ⊗CI [λ, λ]. Here a series of extensions of this matrix Gelfand-Dickey system is derived by means of a generalized Drinfeld-Sokolov reduction defined for the Lie algeb...
متن کاملA note on the appearance of self-dual Yang-Mills fields in integrable hierarchies
A family of mappings from the solution spaces of certain generalized Drinfeld-Sokolov hierarchies to the self-dual Yang-Mills system onR is described. This provides an extension of the well-known relationship between self-dual connections and integrable hierarchies of AKNS and Drinfeld-Sokolov type. 1 Corresponding author’s e-mail: [email protected], phone/fax: (+36) 62 544 368.
متن کاملGauging of Geometric Actions and Integrable Hierarchies of KP Type
This work consist of two interrelated parts. First, we derive massive gauge-invariant generalizations of geometric actions on coadjoint orbits of arbitrary (infinite-dimensional) groups G with central extensions, with gauge group H being certain (infinite-dimensional) subgroup of G. We show that there exist generalized “zero-curvature” representation of the pertinent equations of motion on the ...
متن کاملIntegrable Sigma-models and Drinfeld-Sokolov Hierarchies
Local commuting charges in sigma-models with classical Lie groups as target manifolds are shown to be related to the conserved quantities appearing in the DrinfeldSokolov (generalized mKdV) hierarchies. Conversely, the Drinfeld-Sokolov construction can be used to deduce the existence of commuting charges in these and in wider classes of sigma-models, including those whose target manifolds are e...
متن کاملLie symmetry Analysis and Explicit Exact Dolutions of the Time Fractional Drinfeld-Sokolov-Wilson (DSW) System
In this study coupled system of nonlinear time fractional Drinfeld-Sokolov-Wilson equations, which describes the propagation of anomalous shallow water waves is investigated. The Lie symmetry analysis is performed on the model. Employing the suitable similarity transformations, the governing model is similarity reduced to a system of nonlinear ordinary differential equations with Erdelyi-Kober ...
متن کامل