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arXiv · hep-th/9307110

Notes on $WGL_n$-Algebras and Quantum Miura Transformation

Ya. P. Pugay
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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 $W_l$ 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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Ya. P. Pugay. 1993-07-17. Notes on $WGL_n$-Algebras and Quantum Miura Transformation. https://doi.org/10.1142/s0217751x93001971

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