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arXiv · hep-th/9405116

Universal Drinfeld-Sokolov Reduction and Matrices of Complex Size

Boris Khesin·Feodor Malikov
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Abstract

We construct affinization of the algebra $gl_λ$ 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 $\hat{gl_λ}$ 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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Boris Khesin, Feodor Malikov. 1994-05-31. Universal Drinfeld-Sokolov Reduction and Matrices of Complex Size. https://doi.org/10.1007/bf02101626

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