TITLE: What is Kirillov's method good for?
QUESTION [19 upvotes]: I am planing to study Kirillov's orbit method. I have seen Kirillov's method in several branch of mathematics, for instance, functional analysis, geometry, .... Why is this theory important for mathematics and mathematical physics? Is there any property which connects this theory to several areas of math?
More precisely, I want to know about applications of metaplectic quantization on coadjoint orbit .

REPLY [3 votes]: Let $\hat{G}$ be the set of irreducible representations of a group $G$. Kirillov's method provides a geometric method for understanding $\hat{G}$ as the orbits of $G$ in the dual of the Lie algebra. It is also a means to introducing non-commutative harmonic analysis to engineering.
Tony Dooley from the university of Bath in the UK gave a talk on it and the Kirillov character formula as part of a seminar at my university so it may be productive to check out his homepage.