Supplement to “ Multiresolution analysis on the symmetric group ”
نویسنده
چکیده
Representations. For the purposes of this paper a representation of G over C is a matrix-valued function ρ : G → Cdρ×dρ such that ρ(x)ρ(y) = ρ(xy) for any x, y ∈ G. We call dρ the order or the dimensionality of ρ. Note that ρ(e) = I for any representation. Two representations ρ1 and ρ2 of the same dimensionality d are said to be equivalent if for some invertible T ∈ Cd×d, ρ1(x) = Tρ2(x)T for any x ∈ G. A representation ρ is said to be reducible if it decomposes into a direct sum of smaller representations in the form
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