Secondary quantum Hamiltonian reductions (Q1363116)

The paper deals with conformal algebras, i.e. algebras that contain the Virasoro algebra as a subalgebra. Using secondary Hamiltonian reduction, one can impose extra constraints on a \(W\) algebra obtained by Hamiltonian reduction and derive yet another \(W\) algebra. In the paper it is shown how to quantize this procedure. As an application, the generalized quantum Miura transformation is found. That leads to a large number of new realizations of \(W\) algebras. The authors also show how to use the secondary quantum Hamiltonian reduction to construct linearizations of \(W\) algebras, i.e. the embedding of a \(W\) algebra into a larger algebra which is equivalent to a linear algebra.