W-algebras from soliton equations and Heisenberg subalgebras
- Universidad de Santiago (Spain); and others
The authors derive sufficient conditions under which the {open_quotes}second{close_quotes} Hamiltonian structure of a class of generalized KdV-hierarchies defines one of the classical W-algebras obtained through Drinfel`d-Sokolov Hamiltonian reduction. These integrable hierarchies are associated to the Heisenberg subalgebras of an untwisted affine Kac-Moody algebra. When the principal Heisenberg subalgebra is chosen, the well-known connection between the Hamiltonian structure of the generalized Drinfel`d-Sokolov hierarchies-the Gel`fand-Dickey algebras-and the W-algebras associated to the Casimir invariants of a Lie algebra is recovered. After carefully discussing the relations between the embeddings of A{sub 1} = sl(2, C) into a simple Lie algebra g and the elements of the Heisenberg subalgebras of g, the authors identify the class of W-algebras that can be defined in this way. For A{sub n}, this class only includes those associated to the embeddings labelled by partitions of the form n + 1 = k(m) + q(1) and n + 1 = k(m + 1) + k(m) + q(1). 47 refs.
- OSTI ID:
- 245153
- Journal Information:
- Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 2 Vol. 243; ISSN APNYA6; ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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