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Nonzero Symmetry Classes of Smallest Dimension

Published online by Cambridge University Press:  20 November 2018

G. H. Chan  and
M. H. Lim
G. H. Chan
Affiliation:
Nanyang University, Singapore
M. H. Lim
Affiliation:
University of Malaya, Kuala Lumpur, Malaysia
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Let U be a k-dimensional vector space over the complex numbers. Let ⊗m U denote the mth tensor power of U where m ≧ 2. For each permutation σ in the symmetric group Sm, there exists a linear mapping P(σ) on ⊗mU such that

for all x1, …, xm in U.

Let G be a subgroup of Sm and λ an irreducible (complex) character on G. The symmetrizer

is a projection of ⊗ mU. Its range is denoted by Uλm(G) or simply Uλ(G) and is called the symmetry class of tensors corresponding to G and λ.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 4 , April 1980 , pp. 957 - 968
Copyright
Copyright © Canadian Mathematical Society 1980

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