Quasi-classical limit of BKP hierarchy and W-infinity symmeties

Details Quasi-classical limit of BKP hierarchy and W-infinity symmeties Quasi-classical limit of BKP hierarchy and W-infinity symmeties

1993-01-22

arxiv.org/abs/hep-th/9301090v3

Lett.Math.Phys. 28 (1993) 177-186

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, Kyoto University KUCP-0058/93

Scientific paper

10.1007/BF00745149

Previous results on quasi-classical limit of the KP and Toda hierarchies are now extended to the BKP hierarchy. Basic tools such as the Lax representation, the Baker-Akhiezer function and the tau function are reformulated so as to fit into the analysis of quasi-classical limit. Two subalgebras $\WB_{1+\infty}$ and $\wB_{1+\infty}$ of the W-infinity algebras $W_{1+\infty}$ and $w_{1+\infty}$ are introduced as fundamental Lie algebras of the BKP hierarchy and its quasi-classical limit, the dispersionless BKP hierarchy. The quantum W-infinity algebra $\WB_{1+\infty}$ emerges in symmetries of the BKP hierarchy. In quasi-classical limit, these $\WB_{1+\infty}$ symmetries are shown to be contracted into $\wB_{1+\infty}$ symmetries of the dispersionless BKP hierarchy.

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