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The Schensted and Berele algorithms combinatorially mimic the decompositions of (5J) V with respect to GL^ and Sp2n . Here we present an algorithm which is a common generalization of these two algorithms. "Intermediate symplectic groups" Sp2n m are defined. These groups interpolate between GL^ and Sp^ . We conjecture that there is a decomposition of <g> V with respect to Sp2 which is described by the output of the new algorithm.

A generalized Berele-Schensted algorithm and conjectured Young tableaux for intermediate symplectic groups