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|Paper IPM / M / 459||
By Cayley's theorem, any finite group G of order n can be regarded as a subgroup of the symmetric group $n. Let χ be any irreducible complex character of G and let Vχn (G) denote the symmetry classes of tensors associated with G and
χ. In this paper assuming the Cayley
representation of G, we obtain a formula for the dimension of Vχn (G) and discuss its non-vanishing in general. A necessary condition for the existence of the orthogonal basis of decomposable symmetrized tensors for Vχn (G) is also obtained.
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