Remarks on the star product of functions on finite and compact groups

Details Remarks on the star product of functions on finite and compact groups Remarks on the star product of functions on finite and compact groups

2009-02-26

arxiv.org/abs/0902.4541v1

Phys.Lett.A373:401-408,2009

Physics

Mathematical Physics

17 pages, minor changes with respect to the published version of the paper

Scientific paper

10.1016/j.phys=

Using the formalism of quantizers and dequantizers, we show that the characters of irreducible unitary representations of finite and compact groups provide kernels for star products of complex-valued functions of the group elements. Examples of permutation groups of two and three elements, as well as the SU(2) group, are considered. The k-deformed star products of functions on finite and compact groups are presented. The explicit form of the quantizers and dequantizers, and the duality symmetry of the considered star products are discussed.

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