Discrete Quantum Drinfeld-Sokolov Correspondence

Nonstandard Drinfeld-Sokolov reduction

Subject to some conditions, the input data for the Drinfeld-Sokolov construction of KdV type hierarchies is a quadruplet (A,Λ, d1, d0), where the di are Z-gradations of a loop algebra A and Λ ∈ A is a semisimple element of nonzero d1-grade. A new sufficient condition on the quadruplet under which the construction works is proposed and examples are presented. The proposal relies on splitting the...

Supersymmetric Drinfeld - Sokolov reduction

The Drinfeld-Sokolov construction of integrable hierarchies, as well as its generalizations, may be extended to the case of loop superalge-bras. A sufficient condition on the algebraic data for the resulting hierarchy to be invariant under supersymmetry transformation is given. The method used is a construction of the hierarchies in superspace, where supersymmetry is manifest. Several examples ...

Generalized Drinfeld - Sokolov Hierarchies , Quantum Rings , andW - Gravity

We investigate the algebraic structure of integrable hierarchies that, we propose, underlie models of W-gravity coupled to matter. More precisely, we concentrate on the dispersionless limit of the topological subclass of such theories, by making use of a correspondence between Drinfeld-Sokolov systems, principal sℓ(2) embeddings and certain chiral rings. We find that the integrable hierarchies ...

The Drinfeld Sokolov Holomorphic Bundle and Classical

On Gelfand–Dickey and Drinfeld–Sokolov Systems

We study the connections between Gelfand–Dickey (GD) systems and their modified counterparts, the Drinfeld–Sokolov (DS) systems in the case of general matrix–valued coefficients with entries in a commutative algebra over an arbitrary field. Our main results describe auto–Bäcklund transformations for the GD hierarchy based on Miura–type transformations associated with factorizations of n-th orde...