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Two dimensional string theory is known to have an infinite dimensionalsymmetry, both in the continuum formalism as well as in the matrix modelformalism. We develop a systematic procedure for computing the conservedcharges associated with these symmetries for any configuration of D-branes inthe continuum description. We express these conserved charges in terms of theboundary state associated with the D-brane, and also in terms of the asymptoticfield configurations produced by this D-brane. Comparison of the conservedcharges computed in the continuum description with those computed in the matrixmodel description facilitates identification of the states between these twoformalisms. Using this we put constraints on the continuum description of thehole states in the matrix model, and matrix model description of the blackholes solutions of the continuum theory. We also discuss possiblegeneralization of the construction of the conserved charges to the case ofD-branes in critical string theory.Comment: LaTeX file, 60 page

Symmetries, Conserved Charges and (Black) Holes in Two Dimensional String Theory