Remarks on the Additional Symmetries and W-Constraints in the Generalized KdV Hierarchy

Abstract

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 $1\le n\le p-1$ and $m\ge -1$ with the condition that $\frac{\partial L}{\partial t_{kp}}$ = 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 $\frac{\partial M}{\partial t_{kp}}=0$.

10 pages, Plain Tex

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