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2014 Fiscal Year Final Research Report

Representation-theoretic invariants and moment map

Research Project

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Project/Area Number 23540203
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionTottori University

Principal Investigator

HASHIMOTO Takashi  鳥取大学, 大学教育支援機構, 教授 (90263491)

Project Period (FY) 2011-04-28 – 2015-03-31
Keywordsmoment map / twisted cotangent bundle / symplectic isomorphism / coadjoint orbit / Weil representation / canonical quantization
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.

Free Research Field

表現論

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Published: 2016-06-03  

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