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

Author: Robert A. Proctor
Journal: Trans. Amer. Math. Soc. 324 (1991), 655-692
MSC: Primary 20G05; Secondary 05A15, 20C15
MathSciNet review: 989583
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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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Keywords: Schensted's algorithm, jeu d'tacquin, symplectic groups, tensor representations of Lie groups, Schur functions, group characters
Article copyright: © Copyright 1991 American Mathematical Society

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