2009 Fiscal Year Final Research Report
Representations of elliptic quantum groups and their applications to elliptic special functions
| Project/Area Number |
19540033
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Hiroshima University |
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Principal Investigator |
KONNO Hitoshi Hiroshima University, 大学院・理学研究科, 准教授 (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, 自然科学研究科, 教授 (80164672)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 量子群 / 楕円関数 / 超幾何級数 / アフィン・リー代数 / 可解格子模型 |
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| Research Abstract |
By adding a Hopf algebroid structure to the face type elliptic algebra U_<q,p>(AN^<(1)>), we have formulated it as an elliptic quantum group. Thanks to this structure, we have formulated the intertwining operators on the infinite-dimensional dynamical modules and obtained a consistent result to the previous one derived by using the quasi-Hopf algebra structure. We also have formulated the theta function analogue of the Drinfeld polynomials and shown that they specify the finite-dimensional irreducible dynamical representations uniquely. In the case N=2, we have derived the elliptic analogues of the Clebsch-Gordan coefficients for the tensor product of the finite-dimensional dynamical representations, and shown that they are expressed by using the elliptic hypergeometric series _<12>V_<11>.
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