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An isospectral hierarchy of commutative integrable systems associated with apolynomial spectral problem is proposed. The resulting hierarchy possesses arecursion structure controlled by a hereditary operator. The nonisospectralflows generate the time first order dependent symmetries of the isospectralhierarchy, which constitute Virasoro symmetry algebras together withcommutative symmetries.Comment: 8 pages, Plain-tex, to appear in Prog. Theor. Phy

Coupled Integrable Systems Associated with a Polynomial Spectral Problem and Their Virasoro Symmetry Algebras