On the Fourier transform for a symmetric group homogeneous space
نویسنده
چکیده
By using properties of the Young orthogonal representation, this paper derives a simple form for the Fourier transform of permutations acting on the homogeneous space of n-dimensional vectors, and shows that the transform requires 2n− 2 multiplications and the same number of additions.
منابع مشابه
Fourier Analysis on Semisimple Symmetric Spaces
A homogeneous space X = G/H of a connected Lie group G is called a symmetric homogeneous space if there exists an involution σ of G such that H lies between the fixed point group G and its identity component Go . Example 0. For a connected Lie group G′, put G = G′×G′, σ(g1, g2) ) = (g2, g1) and H = G. Then the homogeneous space X = G/H is naturally isomorphic to G′ by the map (g1, g2) 7→ g1g−1 ...
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