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Stability in modules for classical Lie algebras—a constructive approach

About this Title

G. M. Benkart, D. J. Britten and F. W. Lemire

Publication: Memoirs of the American Mathematical Society
Publication Year: 1990; Volume 85, Number 430
ISBNs: 978-0-8218-2492-4 (print); 978-1-4704-0853-4 (online)
DOI: https://doi.org/10.1090/memo/0430
MathSciNet review: 1010997
MSC: Primary 17B10; Secondary 22E46

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Table of Contents

Chapters

  • Introduction
  • 1. Preliminaries
  • 2. The tensor product realization
  • 3. The dominant weights of $\otimes ^M V(\omega _1, X_r)$
  • 4. The dominant weights of $V(\lambda , X_r)$
  • 5. Dimensions and polynomials
  • 6. Stability of $g_r(\otimes ^{M’} V(\omega _1, X_r)) \otimes g_{r’}(\otimes ^{M''} V(\omega _1, X_r))$
  • 7. Stability of $V(\lambda , X_r) \otimes V(\lambda ’, X_r)$
  • 8. Multiplicities of the dominant weights of $V(\lambda , X_r)$
  • 9. Algorithms and examples