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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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Keywords | moment map / twisted cotangent bundle / symplectic isomorphism / coadjoint orbit / Weil representation / canonical quantization / 運動量写像 / 表現論的不変量 / 随伴多様体 / 捩れ余接束 / 余随伴軌道 / シンプレクティックベクトル空間 / 振動子表現 / （捩れ）運動量写像 / 国際情報交流 |
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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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Report
(5 results)
Research Products
(8 results)
