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

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+∞ and w B 1+∞ of the Winfinity algebrasW1+∞ 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 WB 1+∞ emerges in symmetries of the BKP hierarchy. In quasi-classical limit, these WB 1+∞ symmetries are shown to be contracted into wB 1+∞ symmetries of the dispersionless BKP hierarchy.