Dirac cohomology and geometric quantization
Let be a connected real semisimple Lie group having a finite center and a compact Cartan subgroup with Lie algebra . Let ω be a -invariant symplectic form on . We incorporate Dirac cohomology into the geometric quantization of and study the resulting multiplicity-free unitary -representation on a Hi...
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| Published in | Journal für die reine und angewandte Mathematik Vol. 2016; no. 720; pp. 33 - 50 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
De Gruyter
01.11.2016
|
| Online Access | Get full text |
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| Summary: | Let
be a connected real semisimple Lie group having a finite center
and a compact Cartan subgroup
with Lie algebra
.
Let ω be a
-invariant symplectic form on
.
We incorporate Dirac cohomology into the geometric quantization of
and study the resulting multiplicity-free unitary
-representation
on a Hilbert space
.
We also perform symplectic reduction
of
and show that our quantization method satisfies the principle
“quantization commutes with reduction”. As an application we
construct various models of discrete series. |
|---|---|
| ISSN: | 0075-4102 1435-5345 |
| DOI: | 10.1515/crelle-2014-0050 |