  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.
