Notes on WGLn-Algebras and Quantum Miura Transformation
Ya. P. Pugay
Abstract
We start from the quantum Miura transformation [7] for the W-algebra associated with GL(n) group and find an evident formula for quantum L-operator as well as for the action of Wl currents (l=1,..,n) on elements of the completely degenerated n-dimensional representation. Quantum formulae are obtained through the deformation of the pseudodifferential symbols. This deformation is independent of n and preserves Adler's trace. Our main instrument of the proof is the notation of pseudodifferential symbol with right action which has no counterpart in classical theory.
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