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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Weyl's construction and tensor power decomposition for $G_{2}$


Authors: Jing-Song Huang and Chen-Bo Zhu
Journal: Proc. Amer. Math. Soc. 127 (1999), 925-934
MSC (1991): Primary 22E46, 13A50
MathSciNet review: 1469412
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Abstract: 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
Email: mahuang@uxmail.ust.hk

Chen-Bo Zhu
Affiliation: Department of Mathematics, National University of Singapore, Kent ridge, Singapore 0511
Email: matzhucb@leonis.nus.sg

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04583-9
PII: S 0002-9939(99)04583-9
Keywords: Cayley numbers, invariant theory, tensor power decomposition
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
Article copyright: © Copyright 1999 American Mathematical Society