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Equality of Decomposable Symmetrized Tensors

Published online by Cambridge University Press:  20 November 2018

Russell Merris
Russell Merris*
Affiliation:
Instituto de Fisica e Matemática, Av. Gama Pinto, 2, Lisbon 4, Portugal
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Let V be an n-dimensional vector space over the field F. Let ꕕm V be the rath tensor power of V. If ᓂ ∈ Sm, the symmetric group, there exists a linear operator P (ᓂ1) on ꕕm V such that

for all x1, … , xm ∈ V. (Here, x1 ꕕ … ꕕ xm denotes the decomposable tensor product of the indicated vectors.) If c is any function of Sm taking its values in F, we define

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 5 , 01 October 1975 , pp. 1022 - 1024
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Boerner, H., Representations of groups (American Elsevier, 1970).Google Scholar
2. Marcus, M., Finite dimensional multilinear algebra, Part I (Marcel Dekker, 1973).Google Scholar
3. Marcus, M. and Gordon, W. R., Rational tensor representations of Horn ( V, V) and an extension of an inequality of I. Schur, Can. J. Math. 24 (1972), 686–695.Google Scholar