# 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

#### Citations

##### Publications citing this paper.

SHOWING 1-10 OF 21 CITATIONS

## Symbol Correspondences for Spin Systems

VIEW 9 EXCERPTS

CITES METHODS & BACKGROUND

HIGHLY INFLUENCED

## Invariant symbolic calculus for compact Lie groups

VIEW 1 EXCERPT

CITES BACKGROUND

## Schrödinger model and Stratonovich-Weyl correspondence for Heisenberg motion groups

VIEW 2 EXCERPTS

CITES BACKGROUND & METHODS

## On the Dooley-Rice contraction of the principal series

VIEW 1 EXCERPT

CITES BACKGROUND

## Stratonovich-Weyl correspondence via Berezin quantization

VIEW 2 EXCERPTS

CITES BACKGROUND

## A contraction of the principal series by Berezin-Weyl quantization

VIEW 1 EXCERPT

CITES BACKGROUND

## Berezin transform for non-scalar holomorphic discrete series

VIEW 2 EXCERPTS

CITES BACKGROUND

## Quantization maps, algebra representation, and non-commutative Fourier transform for Lie groups

VIEW 1 EXCERPT

CITES METHODS