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# RepresentationsUnitaryrepresentations of non-compactgroupsSL(2,R)

I've heard that representations (irreducible unitary ones?) representations of noncompact forms of simple Lie groups, e.g. the first example of such a group G being SL(2, R), can be completely described and that there is a discrete and continuous part of the spectrum of L^2(G).

1. How are those representations described?
2. Do all unitary representations come from L^2(G)?
3. How are those related to representation of compact SO(3, R)?
4. What happens in the flat limit between SL(2, R) and SO(3, R)?
5. Is

Also, is it possible to answer the questions above simultaneously for all lie Lie groups, not just SL(2, R)?

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# Representations of non-compact groups

I've heard that representations (unitary ones?) of noncompact forms of simple Lie groups, e.g. SL(2, R), can be completely described and there is a discrete and continuous part.

• How are those described?
• Do all representations come from L^2(G)?
• How are those related to representation of SO(3, R)?
• What happens in the flat limit between SL(2, R) and SO(3, R)?

Is it possible to answer the questions above simultaneously for all lie groups, not just SL(2, R)?