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Integrability of the quantum Boussinesq equation for c=-2 is demonstrated bygiving a recursive algorithm for generating explicit expressions for theinfinite number of commuting charges based on a reduction of the W(infinity)algebra. These charges exist for all spins $s \geq 2$. Likewise, reductions ofthe W(infinity/2) and W((1+infinity)/2) algebras yield the commuting quantumcharges for the quantum KdV equation at c=-2 and c=1/2, respectively.Comment: 11 pages, RevTe

COMMUTING CHARGES OF THE QUANTUM KORTEWEG-DE VRIES AND BOUSSINESQ THEORIES FROM THE REDUCTION OF W∞ AND W1+∞ ALGEBRAS

COMMUTING CHARGES OF THE QUANTUM KORTEWEG-DE VRIES AND BOUSSINESQ THEORIES FROM THE REDUCTION OF W_∞ AND W_1+∞ ALGEBRAS