Super-Yangian double and its central extension

Super Yangian Double and its Central Extension

We introduce super Yangian double DYh̄[gl(m|n)] and its central extension ̂ DYh̄[gl(m|n)]. We give their defining relations in terms of current generators and obtain Drinfeld comultiplication. Queen Elizabeth II Fellow; Email: [email protected] This paper concerns with Drinfeld current realization [1] of super Yangian double DYh̄[gl(m|n)] and its central extension ̂ DYh̄[gl(m|n)]. The Yangian doubl...

SUPER YANGIAN DOUBLE DY (gl(1|1)) AND ITS GAUSS DECOMPOSITION

We extend Yangian double to super (or graded) case and give its Drinfeld generators realization by Gauss decomposition. Quantum algebras(in general meaning, it includes Yangians and quantum affine algebras etc.) are new algebraic structures discovered about ten years ago [1-4], they play important roles in the study of soluble statistical models and quantum fields theory. Quantum universal enve...

Representations of super Yangian

We present in detail the classification of the finite dimensional irreducible representations of the super Yangian associated with the Lie superalgebra gl(1|1). 1 Introduction Many new algebraic structures were discovered in the study of soluble models in statistical mechanics and quantum field theory. Amongst them the quantum groups[1][2] and Yangians[3] are particularly interesting. The forme...

q-AFFINE-YANGIAN DOUBLE CORRESPONDENCE AND FREE BOSON REPRESENTATION OF YANGIAN DOUBLE WITH ARBITRARY LEVEL

We derive a free boson representation of the Yangian double DY~(slN ) with arbitrary level k using the observation that there is a correspondence between the q-affine algebra and Yangian double associated with the same Cartan matrix. Vertex operator and screening currents are not obtained in the same way. Date: January 1997. 0 FREE BOSON REPRESENTATION OF YANGIAN DOUBLE 1

The gl(M|N) Super Yangian and Its Finite Dimensional Representations