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Orthogonal bases of Brauer symmetry classes of tensors for the dihedral group. (English) Zbl 1279.15021
Since the appearance of the paper by B. Wang and M. Gong [Linear Multilinear Algebra 30, No. 1–2, 61–64 (1991; Zbl 0735.15022)], many people have studied the question of when such orthogonal bases exist. So far the results are obtained using an ordinary irreducible character of the given group. In this article, the authors deduce necessary and sufficient conditions for the existence of an orthogonal basis in the case of a dihedral group using the Brauer character of the given group.
Reviewer: Rabeya Basu (Pune)

MSC:
15A69 Multilinear algebra, tensor calculus
20B05 General theory for finite permutation groups
20C20 Modular representations and characters
20C15 Ordinary representations and characters
15A03 Vector spaces, linear dependence, rank, lineability
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