Notes on $WGL_n$-Algebras and Quantum Miura Transformation

Details Notes on $WGL_n$-Algebras and Quantum Miura Transformation Notes on $WGL_n$-Algebras and Quantum Miura Transformation

1993-07-17

arxiv.org/abs/hep-th/9307110v1

Int. J. Mod. Phys. A8 (1993) 5023-5039

Physics

High Energy Physics

High Energy Physics - Theory

Landau-tmp-4-93, 15 pages, Tex (vanilla.sty)

Scientific paper

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 $W_l$ 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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