1993/01/31 by Kanehisa Takasaki · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1007/bf00745149
published as Lett.Math.Phys. 28 (1993) 177-186 · 12 pages, Kyoto University KUCP-0058/93
arxiv created 1993/04/06 · arxiv updated 2009/11/30
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 \WB1+∞ and \wB1+∞ of the W-infinity algebras W1+∞ and w1+∞ are introduced as fundamental Lie algebras of the BKP hierarchy and its quasi-classical limit, the dispersionless BKP hierarchy. The quantum W-infinity algebra \WB1+∞ emerges in symmetries of the BKP hierarchy. In quasi-classical limit, these \WB1+∞ symmetries are shown to be contracted into \wB1+∞ symmetries of the dispersionless BKP hierarchy.