Universal Drinfeld-Sokolov reduction and matrices of complex size

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 ...

Vanishing of Cohomology Associated to Quantized Drinfeld-sokolov Reduction

We prove a vanishing theorem of the cohomology arising from the two quantized Drinfeld-Sokolov reductions (“+” and “−” reduction) introduced by Feigin-Frenkel and Frenkel-Kac-Wakimoto. As a consequence, the vanishing conjecture of Frenkel-Kac-Wakimoto is proved for the “−” reduction and partially for the “+” reduction.

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...