ON THE FOURIER TRANSFORM OF A COMPACT SEMISIMPLE LIE GROUP

@inproceedings{Wildberger1994ONTF,
  title={ON THE FOURIER TRANSFORM OF A COMPACT SEMISIMPLE LIE GROUP},
  author={N. J. Wildberger},
  year={1994}
}
We develop a concrete Fourier transform on a compact Lie group by means of a symbol calculus, or *-product, on each integral co-adjoint orbit. These *-products are constructed by means of a moment map defined for each irreducible representation. We derive integral formulae for these algebra structures and discuss the relationship between two naturally occurring inner products on them. A global Kirillov-type character is obtained for each irreducible representation. The case of SU (2) is treated… CONTINUE READING

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