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Paper   IPM / M / 459
School of Mathematics
  Title:   Non-vanishing and orthogonal basis of symmetry classes of tensors
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
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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