Representations of sl(2,C) in the BGG category O and master symmetries

Abstract

In this paper, we first give a short account on the indecomposable sl(2,C) modules in the Bernstein-Gelfand-Gelfand (BGG) category O. We show these modules naturally arise for homogeneous integrable nonlinear evolutionary systems. We then develop an approach to construct master symmetries for such integrable systems. This method naturally enables us to compute the hierarchy of time-dependent symmetries. We finally illustrate the method using both classical and new examples. We compare our approach to the known existing methods used to construct master symmetries. For the new integrable equations such as a Benjamin-Ono type equation, a new integrable Davey-Stewartson type equation and two different versions of (2+1)-dimensional generalised Volterra Chains, we generate their conserved densities using their master symmetries.

References in corpus (5)

• Integrable properties of the differential-difference Kadomtsev-Petviashvili hierarchy and continuum limits
• Darboux transformation with Dihedral reduction group
• On Classification of Integrable Davey-Stewartson Type Equations
• Towards the classification of integrable differential-difference equations in 2 + 1 dimensions
• Master symmetry and time dependent symmetries of the differential-difference KP equation

Cited by in corpus (4)

• Darboux transformation for the vector sine-Gordon equation and integrable equations on a sphere
• Wave fronts and cascades of soliton interactions in the periodic two dimensional Volterra system
• Two-component integrable generalizations of Burgers equations with nondiagonal linearity
• Generalized symmetries of remarkable (1+2)-dimensional Fokker-Planck equation