Abstract
Presented here is a discussion on the connection between geometric quantization and algebraic quantization. The former procedure relies on a construction of unitary irreducible representations that starts from co-adjoint orbits and uses polarizations, while the latter depends on the purely algebraic characterization of unitary irreducible representations, which is based on central decompositions of von Neumann algebras in involutive duality, and their decompositions in terms of maximal Abelian subalgebras. Intermediate stages of these two quantization methods turn out to be complementary, leading thus to a new characterization of the so-called discrete series representations.
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