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

Proctor, Robert A.

doi:10.1090/S0002-9947-1991-0989583-X

A generalized Berele-Schensted algorithm and conjectured Young tableaux for intermediate symplectic groups
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Trans. Amer. Math. Soc. 324 (1991), 655-692 Request permission

Abstract:

The Schensted and Berele algorithms combinatorially mimic the decompositions of ${ \otimes ^k}V$ with respect to ${\operatorname {GL} _N}$ and ${\operatorname {Sp} _{2n}}$. Here we present an algorithm which is a common generalization of these two algorithms. "Intermediate symplectic groups" ${\operatorname {Sp} _{2n,m}}$ are defined. These groups interpolate between ${\operatorname {GL} _N}$ and ${\operatorname {Sp} _N}$. We conjecture that there is a decomposition of ${ \otimes ^k}V$ with respect to ${\operatorname {Sp} _{2n,m}}$ which is described by the output of the new algorithm.

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