W-algebras from soliton equations and Heisenberg subalgebras

Journal Article · Wed Nov 01 04:00:00 EST 1995 · Annals of Physics (New York)

DOI:https://doi.org/10.1006/aphy.1995.1102· OSTI ID:245153

Fernandez-Pousa, C R; Gallas, M V; Miramontes, J L ^[1]

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1. 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

Related Subjects

66 PHYSICS
ALGEBRA
CONFORMAL GROUPS
FIELD THEORIES
SOLITONS
STRING MODELS