Free-field realization of theWKP(N) algebra |
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Authors: | Yi Cheng |
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Institution: | (1) Department of Mathematics, University of Science and Technology of China, 230026 Hefei, Anhui, People's Republic of China |
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Abstract: | TheW
KP
(N)
algebra has been identified with the second Hamiltonian structure in theNth Hamiltonian pair of the KP hierarchy. In this Letter, by constructing the Miura map that decomposes the second Hamiltonian structure in theNth pair of the KP hierarchy, we show thatW
KP
(N)
can also be decomposed toN independent copies ofW
KP
(1)
algebras, therefore its free-field realization can be worked out by constructing free fields for each copy ofW
KP
(1)
. In this way, the free fields may consist ofN + 2n number of bosons, among them, 2n are in pairs, wheren is an arbitrary integer between 1 andN. We also express the currents ofW
KP
(N)
in terms of the currents ofN —n copies of U(1) andn copies of SL(2,R)
k
algebras with levelk = 1. By reductions, we give similar results forW
(N)
andW
3
(2)
algebra. |
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Keywords: | 35Q53 58F07 17B66 |
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