| Project/Area Number |
15540033
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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, Fac.of Integrated Arts and Sciences, Assoc.Prof., 総合科学部, 助教授 (00291477)
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| Co-Investigator(Kenkyū-buntansha) |
JIMBO Michio Univ.of Tokyo, Graduate School of Math.Sci., Professor, 大学院・数理科学研究科, 教授 (80109082)
TAKEBE Takashi Ochanomizu Univ., Dept.of Math., Assoc.Prof., 理学部, 助教授 (60240727)
MORITA Yoshiyuki Hiroshima University, Graduate School of Science, Assistant, 大学院・理学研究科, 助手 (20243545)
KOJIMA Takeo Nihon University, College of Sci. and Technology, Lecturer, 理工学部, 講師 (80307800)
江口 正晃 広島大学, 総合科学部, 教授 (30037220)
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| Project Period (FY) |
2003 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2005: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2004: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2003: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | Quantum Group / Elliptic Function / Conformal Field Theory / Lie algebra / Hopf algebra / Solvable Lattice Model / ホッブ代数 / Virasoro代数 / affine Lie代数 / Hopf代数 |
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| Research Abstract |
1.Drinfeld realization of B_<q,λ>(g) : For g=A^<(2)>_2, we realized the L-operator of the elliptic quantum group B_<q,λ>(g) in terms of the currents of the elliptic algebra U_<q,p>(g). Then we showed the isomorphism U_<q,p>(g)=^^〜B_<q,λ>(g)【cross product】 C{H^^^} as an associative algebra. Here C{H^^^} denotes some Heisenberg algebra. Futhermore, we constructed the level-1 free field representation of U_<q,p> (A^<(2)>_2), and showed that the vertex operators of U_<q,p>(A^<(2)>_2) provide a realization of the lattice vertex operators of A^<(2)>_2 SOS model in the algebraic analysis formulation.
2.B_<q,λ>(sl^^^_n) and the deformed W_n-algebra : Extending the results in the cases g=A^<(1)>_1,A^<(2)>_2 we showed that a fusion of a pair of the level-1 vertex operators of U_<q,p>(sl^^^_n) implies the basic generating function of the deformed W_<n-1>-algebra.
3.The Vertex-Face Correspondence and the Elliptic Quantum groups : By using the vertex-face correspondence in solvable lattices models, we give an explicite correspondence of the representations of the two types of the elliptic quantum groups, the vertex type A_<q,p>(sl^^^_2) and the face type B_<q,λ>(sl^^^_2). Based on this, we give an algebraic analysis formulation of the fusion eight-vertex model.
4.The Vertex-Face Correspondence and the Elliptic 6j-symbols : We established a new relationship between the vertex-face correspondence intertwining vectors and the elliptic 6j-symbols. We then simplified a proof of the biorthogonal relation, fusion relation and some other relations of the elliptic 6j-symbols. Especially, we derived an equation characterizing the elliptic 6j-symbol, which is similar to the dynamical RLL-relation of the face type elliptic quantum group B_<q,λ>(sl^^^_2).
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