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In this paper, we construct the Virasoro type additional symmetries of a kindof constrained multi-component KP hierarchy and give the Virasoro flow equationon eigenfunctions and adjoint eigenfunctions. It can also be seen that thealgebraic structure of the Virasoro symmetry is kept after discretization fromthe constrained multi-component KP hierarchy to the discrete constrainedmulti-component KP hierarchy.

Virasoro symmetry of the constrained multi-component KP hierarchy and its integrable discretization