Universal Drinfeld-Sokolov Reduction and Matrices of Complex Size

Details Universal Drinfeld-Sokolov Reduction and Matrices of Complex Size Universal Drinfeld-Sokolov Reduction and Matrices of Complex Size

1994-05-18

arxiv.org/abs/hep-th/9405116v2

Commun.Math.Phys. 175 (1996) 113-134

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, no figures

Scientific paper

10.1007/BF02101626

We construct affinization of the algebra $gl_{\lambda}$ of ``complex size'' matrices, that contains the algebras $\hat{gl_n}$ for integral values of the parameter. The Drinfeld--Sokolov Hamiltonian reduction of the algebra $\hat{gl_{\lambda}}$ results in the quadratic Gelfand--Dickey structure on the Poisson--Lie group of all pseudodifferential operators of fractional order. This construction is extended to the simultaneous deformation of orthogonal and simplectic algebras that produces self-adjoint operators, and it has a counterpart for the Toda lattices with fractional number of particles.

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