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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Weyl’s construction and tensor power decomposition for $G_2$
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by Jing-Song Huang and Chen-Bo Zhu PDF
Proc. Amer. Math. Soc. 127 (1999), 925-934 Request permission


Let $V$ be the 7-dimensional irreducible representations of $G_{2}$. We decompose the tensor power $V^{\otimes n}$ into irreducible representations of $G_{2}$ and obtain all irreducible representations of $G_{2}$ in the decomposition. This generalizes Weyl’s work on the construction of irreducible representations and decomposition of tensor products for classical groups to the exceptional group $G_{2}$.
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Additional Information
  • Jing-Song Huang
  • Affiliation: Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
  • MR Author ID: 304754
  • Email:
  • Chen-Bo Zhu
  • Affiliation: Department of Mathematics, National University of Singapore, Kent ridge, Singapore 0511
  • MR Author ID: 305157
  • ORCID: 0000-0003-3819-1458
  • Email:
  • Received by editor(s): March 25, 1997
  • Received by editor(s) in revised form: July 7, 1997
  • Additional Notes: The first named author was partially supported by NSF Grant DMS 9306138 and RGC Competitive Earmarked Research Grant HKUST 588/94P
  • Communicated by: Roe Goodman
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 925-934
  • MSC (1991): Primary 22E46, 13A50
  • DOI:
  • MathSciNet review: 1469412