2014 Fiscal Year Final Research Report
Construction of path models for modules of critical level over affine Lie algebras
| Project/Area Number |
23740003
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Keywords | 量子アフィン代数 / アフィン・リー代数 / 結晶基底 / クリスタル / パス模型 / 量子 Bruhat グラフ / 半無限 Bruhat グラフ / エクストリーマル・ウェイト加群 |
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| Outline of Final Research Achievements |
(1) We described level-zero Lakshmibai-Seshadri (LS) paths in terms of the (parabolic) quantum Bruhat graph. As an application, we described the degree function (= energy function) on the crystal of level-zero LS paths in terms of the weights of shortest directed paths in the quantum Bruhat graph.
(2) We introduced semi-infinite LS paths in terms of the semi-infinite Bruhat order (and semi-infinite Bruhat graph), which is closely related to irreducible highest weight representations of critical level, and then we proved that the crystal of semi-infinite LS paths is isomorphic, as a crystal, to the crystal basis of the extremal weight module.
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| Free Research Field |
リー代数・量子群の組合せ論的表現論
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