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 with respect to and . Here we present an algorithm which is a common generalization of these two algorithms. "Intermediate symplectic groups" are defined. These groups interpolate between and . We conjecture that there is a decomposition of with respect to which is described by the output of the new algorithm.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1991-0989583-X

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