Secondary Quantum Hamiltonian Reduction

Details Secondary Quantum Hamiltonian Reduction Secondary Quantum Hamiltonian Reduction

1995-03-07

arxiv.org/abs/hep-th/9503042v3

Commun.Math.Phys. 185 (1997) 509-541

Physics

High Energy Physics

High Energy Physics - Theory

33 pages, LATEX. Final version, including proof of conjecture. Accepted for publication in Comm. Math. Phys

Scientific paper

10.1007/s002200050101

Recently, it has been shown how to perform the quantum hamiltonian reduction in the case of general $sl(2)$ embeddings into Lie (super)algebras, and in the case of general $osp(1|2)$ embeddings into Lie superalgebras. In another development it has been shown that when $H$ and $H'$ are both subalgebras of a Lie algebra $G$ with $H'\subset H$, then classically the $W(G,H)$ algebra can be obtained by performing a secondary hamiltonian reduction on $W(G,H')$. In this paper we show that the corresponding statement is true also for quantum hamiltonian reduction when the simple roots of $H'$ can be chosen as a subset of the simple roots of $H$. As an application, we show that the quantum secondary reductions provide a natural framework to study and explain the linearization of the $W$ algebras, as well as a great number of new realizations of $W$ algebras.

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