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28 March 2024
 
  » arxiv » hep-th/9312040

 Article overview


$W$--geometry of the Toda systems associated with non-exceptional simple Lie algebras
Jean-Loup Gervais ; Mikhail V. Saveliev ;
Date 6 Dec 1993
Journal Commun.Math.Phys. 180 (1996) 265-296
Subject High Energy Physics - Theory; Quantum Algebra | hep-th math.QA
AbstractThe present paper describes the $W$--geometry of the Abelian finite non-periodic (conformal) Toda systems associated with the $B,C$ and $D$ series of the simple Lie algebras endowed with the canonical gradation. The principal tool here is a generalization of the classical Plücker embedding of the $A$-case to the flag manifolds associated with the fundamental representations of $B_n$, $C_n$ and $D_n$, and a direct proof that the corresponding Kähler potentials satisfy the system of two--dimensional finite non-periodic (conformal) Toda equations. It is shown that the $W$--geometry of the type mentioned above coincide with the differential geometry of special holomorphic (W) surfaces in target spaces which are submanifolds (quadrics) of $CP^N$ with appropriate choices of $N$. In addition, these W-surfaces are defined to satisfy quadratic holomorphic differential conditions that ensure consistency of the generalized Plücker embedding. These conditions are automatically fulfiled when Toda equations hold.
Source arXiv, hep-th/9312040
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