Algebraic analysis of integrable models
| Project/Area Number |
23340039
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Rikkyo University |
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Principal Investigator |
JIMBO Michio 立教大学, 理学部, 教授 (80109082)
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| Project Period (FY) |
2011-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥9,100,000 (Direct Cost: ¥7,000,000、Indirect Cost: ¥2,100,000)
Fiscal Year 2014: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2013: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2012: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2011: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
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| Keywords | フェルミオン基底 / ６頂点模型 / サイン・ゴルドンモデル / 形状因子 / ボレル部分代数 / 量子トロイダル代数 / ベーテ仮説 / フェルミオン構造 / 相関関数 / 可積分場の理論 / XXZ模型 / 共形場理論 / 量子アフィン代数 |
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| Outline of Final Research Achievements |
The main achievements are the following.(1) We identified the continuum limit of our fermionic basis in solvable lattice models with those employed previously in the enumeration of form factors, thereby establishing the fermionic picture in field theory. (2) We studied representations in “category O” of Borel subalgebras of quantum affine algebras, and classified the irreducible objets by highest weights. (3) We constructed a family of irreducible representations of quantum toroidal algebras by an elementary method. We also diagonalized the transfer matrix acting on the Fock space, and established the Bethe ansatz.
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Report
(5 results)
Research Products
(23 results)
