On the orthogonal basis of the symmetry classes of tensors associated with certain characters
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چکیده
منابع مشابه
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Non-Vanishing and Orthogonal Basis of Symmetry Classes of Tensors
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 V n χ (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 V n χ (G) and discuss its non-vanishing in general. A necessary...
متن کاملSome Non-trivial Symmetry Classes of Tensors Associated with Certain Characters
Let G be a finite group and Ω a set of n elements. Assume that G acts faithfully on Ω and let V be a vector space over the complex field C, with dimV = m ≥ 2. It is shown that for each irreducible constituent χ of permutation character of G, the symmetry class of tensors associated with G and χ is non-trivial. This extends a result of Merris and Rashid (see [6, Theorem 2]).
متن کاملSymmetry classes of polynomials associated with the dihedral group
In this paper, we obtain the dimensions of symmetry classes of polynomials associated with the irreducible characters of the dihedral group as a subgroup of the full symmetric group. Then we discuss the existence of o-basis of these classes.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2001
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(01)00329-9