The special values of the standard L-functions for \operatorname{GSp}_{2n} \times\operatorname{GL}_1.

We prove the expected algebraicity property for the critical values of character twists of the standard L-function associated to vector-valued holomorphic Siegel cusp forms of archimedean type (k_1, k_2, ..., k_n), where k_n \ge n+1 and all k_i are of the same parity. For the proof, we use an explicit integral representation to reduce to arithmetic properties of differential operators on vector-valued nearly holomorphic Siegel cusp forms. We establish these properties via a representation-theoretic approach. [ABSTRACT FROM AUTHOR]