I'm a PhD student in mathematical physics and I happen to need some elements of Kirillov's "orbit method" for producing representations of Lie groups. I'm familiar with symplectic geometry, geometric quantization and coadjoint orbits. As regards the present question, I use the terminology of Witten, "Coadjoint orbits of the Virasoro group".

Specifically, my questions are the following (questions 2 and 3 are the most important ones to me; even a partial answer may be satisfactory!):

- What is the definition of "unipotent representation" for SL(2,R), regardless of geometric quantization?
- Are all unipotent representations of SL(2,R) known and classified?
- If yes, is it known how to reproduce these representations by geometric quantization of the "cone-like" coadjoint orbits of SL(2,R)?
- Same questions for any non-compact, semi-simple Lie group.

I've tried to find an answer by Googling "unipotent representations SL(2,R)" and similar keywords, but the only search results I got were research papers that were too advanced for me :-( In particular, the paper "Unipotent Representations of Complex Semisimple Groups" by Barbasch and Vogan provides a definition of "unipotent representation" (definition 1.17 of the paper), but it is a bit obscure to me... I hope there exists a simpler reformulation of this definition.

(By the way, I've posted the same question on the math stack exchange, but I don't know how the stack exchange and overflow communities communicate.)