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Regular principal models of split semisimple Lie groups
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Meng-Kiat Chuah
Published/Copyright:
July 1, 2008
Abstract
Let G be a semisimple Lie group. Geometric quantization is a machinery which transforms a symplectic G-manifold X to a unitary G-representation 
. Let C be a Cartan subgroup of G, and L the stabilizer of an element in the Lie algebra of C. Let 
, where Lss is the commutator subgroup of L, and 
is the Lie algebra of the centralizer of L in C. When G is split, we perform geometric quantization to G × H-invariant symplectic forms on X. As a result, we construct a regular principal model in the sense that every regular principal series representation of G occurs once in . We also perform symplectic reduction to X and show that “quantization commutes with reduction”.
Received: 2006-05-04
Revised: 2007-08-10
Published Online: 2008-07-01
Published in Print: 2008-October
© Walter de Gruyter Berlin · New York 2008
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Articles in the same Issue
- On the p-parts of quadratic Weyl group multiple Dirichlet series
- Characterization of SUq(ℓ + 1)-equivariant spectral triples for the odd dimensional quantum spheres
- The congruence kernel of an arithmetic lattice in a rank one algebraic group over a local field
- Lie ideals: from pure algebra to C*-algebras
- Strongly pseudoconvex homogeneous domains in almost complex manifolds
- The Cuntz semigroup as an invariant for C*-algebras
- Regular principal models of split semisimple Lie groups
- Asymptotic Abelianness, weak mixing, and property T
