2014 Fiscal Year Final Research Report
Representation-theoretic invariants and moment map
| Project/Area Number |
23540203
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Tottori University |
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Principal Investigator |
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Keywords | moment map / twisted cotangent bundle / symplectic isomorphism / coadjoint orbit / Weil representation / canonical quantization |
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| Outline of Final Research Achievements |
I showed that a twisted moment map provides a symplectic isomorphism from a twisted cotangent bundle on the Grassmann variety of complex reductive linear Lie groups G, which one constructs by patching locally trivial bundles using affine transformation that is induced from the twisted moment map, onto complex coadjoint G-orbit, and that the isomorphism, in fact, gives a moment map on the twisted cotangent bundle. I also construcred an embedding of coadjoint orbit under noncompact real forms G_0 of G into the (twisted) cotangent bundle in terms of the twisted moment map and the highest weight vector of unitary representation of G_0.
Moreover, I showed that the canonical quantization of the moment map on symplectic vector spaces gives us the oscillator (or Segal-Shale-Weil) representations and that the images of Lagrangian subspaces chosen in the quantization coincides with the associated varieties of the representations.
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| Free Research Field |
表現論
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