Weyl's construction and tensor power decomposition for
Authors:
Jing-Song Huang and Chen-Bo Zhu
Journal:
Proc. Amer. Math. Soc. 127 (1999), 925-934
MSC (1991):
Primary 22E46, 13A50
DOI:
https://doi.org/10.1090/S0002-9939-99-04583-9
MathSciNet review:
1469412
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be the 7-dimensional irreducible representations of
. We decompose the tensor power
into irreducible representations of
and obtain all irreducible representations of
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
.
- [H] Roger Howe, Perspectives on invariant theory: Schur duality, multiplicity-free actions and beyond, The Schur lectures (1992) (Tel Aviv), Israel Math. Conf. Proc., vol. 8, Bar-Ilan Univ., Ramat Gan, 1995, pp. 1–182. MR 1321638
- [FH] William Fulton and Joe Harris, Representation theory, Graduate Texts in Mathematics, vol. 129, Springer-Verlag, New York, 1991. A first course; Readings in Mathematics. MR 1153249
- [MP] W. G. McKay and J. Patera, Tables of dimensions, indices, and branching rules for representations of simple Lie algebras, Lecture Notes in Pure and Applied Mathematics, vol. 69, Marcel Dekker, Inc., New York, 1981. MR 604363
- [S] Gerald W. Schwarz, Invariant theory of 𝐺₂ and 𝑆𝑝𝑖𝑛₇, Comment. Math. Helv. 63 (1988), no. 4, 624–663. MR 966953, https://doi.org/10.1007/BF02566782
- [W] H. Weyl, The classical groups, Princeton Mathematical Series, Princeton University Press, 1939; second edition, 1946; third edition, 1966. MR 1:42c
- [Wo]
Y.-K. Wong, The First Fundamental Theorem of Covariants for
and
, Yale thesis, Yale University, 1995.
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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:
https://doi.org/10.1090/S0002-9939-99-04583-9
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