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This paper claims to have a concrete formula for Haar measure on SL(2,C), in section 3:
www-users.cse.umn.edu/~garrett/m/v/S…
I got this by typing “Haar measure on sl(2,C)” into Google.

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That’s as far as I got too!
I’ll post a short thread explaining why this is useful for physics later this evening.

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They are trying to get the volume form by writing every element of G as exp(k) exp(a) exp(k’) where k,k’ are in the Lie algebra of a maximal compact subgroup and a is in the Lie algebra of a maximal abelian subgroup.
en.wikipedia.org/wiki/Cartan_de…

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