Partial Dirac cohomology and tempered representations |
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| Institution: | 1. Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan;2. School of Science and Engineering, Chinese University of Hong Kong, Shenzhen, China;3. Department of Mathematics, University of California, Berkeley CA 94720-3840, USA |
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| Abstract: | The tempered representations of a real reductive Lie group G are naturally partitioned into series associated with conjugacy classes of Cartan subgroups H of G. We define partial Dirac cohomology, apply it for geometric construction of various models of these H–series representations, and show how this construction fits into the framework of geometric quantization and symplectic reduction. |
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| Keywords: | Real reductive group Tempered representation Dirac cohomology Geometric quantization |
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