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Paper   IPM / M / 459
School of Mathematics
Title:   Non-vanishing and orthogonal basis of symmetry classes of tensors
Author(s):
 1 M. R. Darafsheh 2 M. R. Pournaki
Status:   Published
Journal: Southeast Asian Bull. Math.
No.:  4
Vol.:  24
Year:  2000
Pages:   525-531
Publisher(s):   Springer-Verlag
Supported by:  IPM
Abstract:
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.