On the classical W[sub n]([sup l]) algebras

Journal Article · Wed Sep 30 04:00:00 EDT 1992 · International Journal of Modern Physics A; (United States)

DOI:https://doi.org/10.1142/S0217751X92002751· OSTI ID:7158953

Depireux, D A; Mathieu, P ^[1]

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1. Laval Univ., Quebec City, PQ (Canada). Dept. de Physique

In this paper, the authors analyze the W[sub N][sup (l)] algebras according to their conjectured realization as the second Hamiltonian structure of the integrable hierarchy resulting from the interchange of x and t in the l th flow of the sl(N) KdV hierarchy. The W[sub 4][sup (3)] algebra is derived explicitly along these lines, thus providing further support for the conjecture. This algebra is found to be equivalent to that obtained by the method of Hamiltonian reduction. Furthermore, its twisted version reproduces the algebra associated to a certain nonprincipal embedding of sl(2) into sl(4), or equivalently, the u(2) quasi-superconformal algebra. General aspects of the W[sub N][sup (l)] algebras are also presented. The authors point out in particular that the x [leftrightarrow] t interchange approach of the W[sub N][sup (l)] algebra appears straightforward only when N and l are coprime.

• OSTI ID: 7158953
• Journal Information: International Journal of Modern Physics A; (United States), Journal Name: International Journal of Modern Physics A; (United States) Vol. 7:24; ISSN IMPAEF; ISSN 0217-751X
• Country of Publication: United States
• Language: English

Related Subjects

661100 -- Classical & Quantum Mechanics-- (1992-)
662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
CLASSICAL MECHANICS
CONFORMAL GROUPS
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LIE GROUPS
MATHEMATICAL OPERATORS
MATHEMATICS
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