2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/53576It 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.plain tex, 15 pages, IMSC-93/11, SBNC-06/93High Energy Physics - Theorytext