| Project/Area Number |
26400046
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tokyo University of Marine Science and Technology |
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Principal Investigator |
Konno Hitoshi 東京海洋大学, 学術研究院, 教授 (00291477)
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| Co-Investigator(Renkei-kenkyūsha) |
JIMBO MICHIO 立教大学, 理学部, 教授 (80109082)
NOUMI MASATOSHI 神戸大学, 大学院理学研究科, 教授 (80164672)
MIMACHI KATSUHISA 大阪大学, 大学院情報科学研究科, 教授 (40211594)
OSHIMA KAZUYUKI 愛知工業大学, 基礎教育センター, 准教授 (30547980)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 楕円量子群 / 楕円Ruijsenaars模型 / 楕円q-KZ方程式 / 量子行列式 / 変形W代数 / Macdonald対称関数 / 楕円超幾何関数 / Rujisenaars模型 / q-KZ方程式 / ヘッケ環 / Macdonald多項式 / アフィン リー環 / 超幾何関数 / 量子群 / ホップ代数 / 楕円関数 / KZ方程式 / 特殊関数 / 楕円量子KZ方程式 / W代数 / アフィンリー環 / Hecke環 / Ruijsenaars模型 |
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| Outline of Final Research Achievements |
We have formulated the quantum determinant as well as the quantum minor determinants of the L-operators for the face type elliptic quantum group U_q,p(gl_N). We have also obtained a formula for the elliptic half currents in terms of the quantum minor determinants. We then have completed a proof of the isomorphism between U_q,p(gl_N) and the central extension E_q,p(gl_N) of Felder’s elliptic quantum group. In addition, we have obtained formal elliptic hypergeometric integral solutions to the face type elliptic q-KZ equation and associated elliptic weight functions by considering the traces of the product of the intertwining operators of the level-1 U_q,p(sl_N)-modules.
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