Construction of path models for modules of critical level over affine Lie algebras
Project/Area Number |
23740003
|
Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Algebra
|
Research Institution | University of Tsukuba |
Principal Investigator |
|
Project Period (FY) |
2011-04-28 – 2015-03-31
|
Project Status |
Completed (Fiscal Year 2014)
|
Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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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 / Lakshmibai-Seshadri パス / Macdonald 多項式 / 半無限 Bruhat 順序 / Lakshmibai-Seshadriパス / Mirkovic-Vilonen多面体 / quantum Bruhat graph |
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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Report
(5 results)
Research Products
(20 results)