Convolution and Star-Products on Compact Groups

For compact groups G, a star-product is defined using the family Ĝ of unitary irreducible representations of G, given by (The equation is abbreviated) whereλ∈Ĝ and A_f is a certain operator corresponding to the function f ∈ C^∞(G). We show that a certain sum of these star-products over Ĝ is equal to the usual convolution product of functions in L^1(G), thereby establishing a direct link between a geometric object, the star-product and a harmonic analytic object, that of convolution. For instance, the decomposition of the regular representation of G in L^2(G) is easily read off from the sum involving the star-products.

並列關鍵字

Compact groups ； Deformation quantization ； Star-products ； Unitary representations of groups ； Convolution

國際替代計量

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