Geodesic
$W_\infty$ -- a~geometric approach
Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 2, pp. 273-285

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A brief review is given of an adaptation of the coadjoint orbit method appropriate for the study of models with infinite-dimensional symmetry groups. It is illustrated on several examples, including derivation of the WZNW action of induced $D=2$ $(N,0)$ supergravity. As the main application, we present the geometric action on a generic coadjoint orbit of the deformed group of area-preserving diffeomorphisms. This action is precisely the anomalous effective WZNW action of $D=2$ matter fields coupled to a chiral $W_\infty$ gravity background. Similar actions are given which produce the KP hierarchy as on-shell equations of motion. 
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     author = {E. Nissimov and S. Pacheva},
     title = {$W_\infty$ -- a~geometric approach},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {273--285},
     publisher = {mathdoc},
     volume = {93},
     number = {2},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_93_2_a6/}
}
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E. Nissimov; S. Pacheva. $W_\infty$ -- a~geometric approach. Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 2, pp. 273-285. http://geodesic.mathdoc.fr/item/TMF_1992_93_2_a6/