Additional symmetries of the $p$-reduced KP hierarchy are generated by the Lax operator $L$ and another operator $M$, satisfying $res (M^n L^{ m+n/p})$ = 0 for $1 \leq n \leq p-1$ and $m \geq -1$ with the condition that ${ \partial L \over { \partial t_{ kp}}}$ = 0, $k$ = 1, 2,..... We show explicitly that the generators of these additional symmetries satisfy a closed and consistent W-algebra only when we impose the extra condition that ${ \partial M \over { \partial t_{ kp}}} = 0$.
Categories: hep-th
