Abstract
The theory of the relationship between the symmetric group on a symbols, Σa, and the general linear group in n-dimensions, GL(n), was greatly developed by Weyl [4] who, in this connection, made use of tensor representations of GL(n). The set of mixed tensorsforms the basis of a representation of GL(n) if all the indices may take the values 1, 2, …, n, and if the linear transformationis associated with every non-singular n × n matrix A. The representation is irreducible if the tensors are traceless and if the sets of covariant indices (α)a and contra variant indices (β)b themselves form the bases of irreducible representations (IRs) of Σa and Σb, respectively. These IRs of Σa and Σb may be specified by Young tableaux [μ]a and [v]b in the usual way [4].
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