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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

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A generalized Berele-Schensted algorithm and conjectured Young tableaux for intermediate symplectic groups
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by Robert A. Proctor PDF
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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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 324 (1991), 655-692
  • MSC: Primary 20G05; Secondary 05A15, 20C15
  • DOI: https://doi.org/10.1090/S0002-9947-1991-0989583-X
  • MathSciNet review: 989583