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THE DESCRIPTION OF THE CAPELLI ELEMENTS WITH A PARAMETER FOR CLASSICAL LIE ALGEBRAS IN TERMS OF SYMMETRIZED DETERMINANT
We construct the Capelli elements Ck(u) = C(1k)(u) (k = 1, . . . , n) with a parameter u for the symplectic Lie algebras and orthogonal Lie algebras. They correspond to factorial Schur functions with parameter u attached to the column partitions (1k). We also give explicit formulas for …