10. Compute the Plancherel measure The measure on O(G) arising when
μ on G. the Lebesgue measure on
is decomposed into canonical
measures on coadjoint orbits.
These short instructions are developed in Chapter 3 and illustrated in
the worked-out examples in the main text.
Finally, a technical remark. I am using the standard sign to signal
the end of a proof (or the absence of proof). I also use less standard notation:
♦ – the end of an example;
♥ – the end of a remark;
♣ – the end of an exercise;
♠ – the end of a warning about a possible mistake or misunderstand-
The most diﬃcult exercises and parts of the text are marked by an