1999 Fiscal Year Final Research Report Summary
Solvable Lattice Models and Elliptic Quantum Groups
| Project/Area Number |
10440042
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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 |
Basic analysis
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| Research Institution | KYOTO UNIVERSITY |
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Principal Investigator |
JIMBO Michio Kyoto University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (80109082)
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| Co-Investigator(Kenkyū-buntansha) |
KONNO Hitoshi Hiroshima Univ., Culture and the Humanities Associate Professor, 総合科学部, 助教授 (00291477)
SHIMIZU Yuji Kyoto University, Graduate School of Science, Lecturer, 大学院・理学研究科, 講師 (80187468)
SHIOTA Takahiro Kyoto University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (20243008)
ODAKE Satoru Shinsyu Univ, Fuculty of Science, Associate Professor, 理学部, 助教授 (40252051)
SHIRAISHI Junichi Univ. of Tokyo, Graduate School of Mathematical Science, Associate Professor, 大学院・数理科学研究科, 助教授 (20272536)
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| Project Period (FY) |
1998 – 1999
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| Keywords | elliptic quantum groups / solvable lattice models / free field representation / deformed Virasoro algebras / conformal field theory / invariant theory / matrix models |
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| Research Abstract |
Results concerning solvable models and elliptic quantum groups :
(1)Fronsdal observed earlier that the elliptic quantum groups are nothing but quasi-Hopf twists of quantum affine algebras. Following this idea, we constructed explicitly the twist defining elliptic quantum groups in the form of an infinite product of the universal R matrix. Our construction settled some conjectures previously made by Foda et al. on vertex type elliptic quantum groups.
(2)We obtained an L operator in the Fock space representation and interpreted Lukyanov-Pugai's vertex operators as intertwiners for elliptic quantum groups.
(3)We constructed free field representations for solvable lattice models which correspond to integrable perturbations of conformal field theories : the dilute AィイD2LィエD2 models and the ABF models in regime II.
Other results :
(4)Umeda reformulated and proved Cappelli type identities mentioned by Turnbull, as an identity of invariant differential operators.
(5)Shiota showed that ceretain Fredholm determinants arising in the Baker-Akhiezer functions in the KP hierarchy are expressible as ratios of tau functions.
(6)Shimizu gave a reformulation of the stress-energy tensorsin conformal field theory as Hamiltonian action on the cotangent bundle of the moduli spaces of Riemann surfaces.
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