$SL(n,R)$ KDV Hierarchy and its Nonpolynomial Realization Through Kac-Moody Currents

Details $SL(n,R)$ KDV Hierarchy and its Nonpolynomial Realization Through Kac-Moody Currents $SL(n,R)$ KDV Hierarchy and its Nonpolynomial Realization Through Kac-Moody Currents

1993-06-24

arxiv.org/abs/hep-th/9306126v1

Physics

High Energy Physics

High Energy Physics - Theory

plain tex, 15 pages, IMSC-93/11, SBNC-06/93

Scientific paper

It is shown that $SL(n,R)$ KdV hierarchy can be expressed as definite nonpolynomials in Kac Moody currents and their derivatives by the action of Borel subgroup of $SL(n,R)$ on the phase space of centrally extended $sl(n,R)$ Kac Moody currents. Construction of Lax pair is shown, confirming Drinfeld Sokolov type Hamiltonian reduction. This suggests an example of a moduli space with symplectic structure corresponding to extended conformal symmetries.

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