  Two dimensional string theory is known to have an infinite dimensional
symmetry, both in the continuum formalism as well as in the matrix model
formalism. We develop a systematic procedure for computing the conserved
charges associated with these symmetries for any configuration of D-branes in
the continuum description. We express these conserved charges in terms of the
boundary state associated with the D-brane, and also in terms of the asymptotic
field configurations produced by this D-brane. Comparison of the conserved
charges computed in the continuum description with those computed in the matrix
model description facilitates identification of the states between these two
formalisms. Using this we put constraints on the continuum description of the
hole states in the matrix model, and matrix model description of the black
holes solutions of the continuum theory. We also discuss possible
generalization of the construction of the conserved charges to the case of
D-branes in critical string theory.
