A Remark on Random Vectors and Irreducible Representations

10/29/2021

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by   Alexander Kushkuley, et al.

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It was observed in [1] that the expectation of a squared scalar product of two random independent unit vectors that are uniformly distributed on the unit sphere in R^n is equal to 1/n. It is shown in this paper, that this is a characteristic property of random vectors defined on invariant probability subspaces of unit spheres in irreducible real representations of compact Lie groups.