The Algebra of Differential Operators on the Circle and W (q) KP
Abstract
Radul has recently introduced a map from the Lie algebra of differential operators on the circle to
W
n
. In this note we extend this map to
W
(q)
KP
, a recently introduced one-parameter deformation of
W
KP
---the second hamiltonian structure of the KP hierarchy. We use this to give a short proof that
W
∞
is the symmetry algebra of additional symmetries of the KP equation.