$W_{\infty}$--Geometry and Associated Continuous Toda System

Details $W_{\infty}$--Geometry and Associated Continuous Toda System $W_{\infty}$--Geometry and Associated Continuous Toda System

1993-05-27

arxiv.org/abs/hep-th/9305152v1

Phys.Lett. B313 (1993) 55-58

Physics

High Energy Physics

High Energy Physics - Theory

6 pages, no figure report\# ETH-TH/93-21

Scientific paper

10.1016/0370-2693(93)91190-X

We discuss an infinite--dimensional k\"ahlerian manifold associated with the area--preserving diffeomorphisms on two--dimensional torus, and, correspondingly, with a continuous limit of the $A_r$--Toda system. In particular, a continuous limit of the $A_r$--Grassmannians and a related Pl\"ucker type formula are introduced as relevant notions for $W_{\infty}$--geometry of the self--dual Einstein space with the rotational Killing vector.

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