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The Classical limit of W algebras

Jose M. Figueroa-O'Farrill
(
- Bonn U.
)
,
Eduardo Ramos
(
- Leuven U.
)

Feb, 1992

8 pages

Published in:

Phys.Lett.B 282 (1992) 357-364

Published: 1992

e-Print:

hep-th/9202040 [hep-th]

DOI:

10.1016/0370-2693(92)90652-K

Report number:

KUL-TF-92-5,
BONN-HE-92-03

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Abstract:

We define and compute explicitly the classical limit of the realizations of

W_n

appearing as hamiltonian structures of generalized KdV hierarchies. The classical limit is obtained by taking the commutative limit of the ring of pseudodifferential operators. These algebras---denoted

w_n

---have free field realizations in which the generators are given by the elementary symmetric polynomials in the free fields. We compute the algebras explicitly and we show that they are all reductions of a new algebra

w_{\rm KP}

, which is proposed as the universal classical

W

-algebra for the

w_n

series. As a deformation of this algebra we also obtain

w_{1+\infty}

, the classical limit of

W_{1+\infty}

.

algebra: W(N)
approximation: classical
Korteweg-de Vries equation: hierarchy
Hamiltonian formalism
operator: Lax

References(17)

Figures(0)

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