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Universal Drinfeld-Sokolov Reduction and Matrices of Complex Size

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arxiv hep-th/9405116 v2 pith:42GFZKP2 submitted 1994-05-18 hep-th math.QA

classification hep-thmath.QA
keywords algebraalgebrascomplexfractionallambdamatricesoperatorsreduction
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abstract

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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