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KAKEN_25400073seika.pdf
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Download
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:169.9 KB
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| Last updated |
:Oct 31, 2019 |
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Total downloads since Oct 31, 2019 : 422
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| Title |
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シンプレクティック構造の変形とそのユニタリー表現論への応用
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シンプレクティック コウゾウ ノ ヘンケイ ト ソノ ユニタリー ヒョウゲンロン エノ オウヨウ
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Shinpurekutikku kōzō no henkei to sono yunitarī hyōgenron eno ōyō
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A deformation of symplectic structures and its application for unitary representations
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池田, 薫
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イケダ, カオル
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Ikeda, Kaoru
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慶應義塾大学・経済学部 (日吉)・教授
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Research team head
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科研費研究者番号 : 40232178
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2019
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科学研究費補助金研究成果報告書
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2018
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簡約Lie群の既約ユニタリー表現の一般的な構成法の確立に向けて研究を行った. Gを簡約Lie群PをGの放物型部分群とし旗多様体X=G/Pを考える. XはWeyl群Wでパラメトライズされた開被覆で覆われる. さてBをPに含まれるBorel部分群とする. bをBのLie環とする. Λをshift operaterとする. GのLie環gのaffaine部分空間LaxをΛ+bで定義する. Xの元umodPに対してLaxの元をコンパニオン埋め込みにより定義したtarget空間によるσモデルを考えた。
We study the geometrical quantization to construct irreducible unitary representations of reductive Lie groups. Let G be a reductive Lie group and B be its Borel subgroup. We consider the parabolic subgroup P which includes B. We study the flag variety X=G/P. The flag variety X is constructed by gluing |W| affine spaces, where W is Weyl group. Each affine space is isomorphic to Heisenberg group.
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研究種目 : 基盤研究(C)(一般)
研究期間 : 2013～2018
課題番号 : 25400073
研究分野 : 可積分系
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