| Co-Investigator(Kenkyū-buntansha) |
TAKEBE Takashi Ochanomizu Univ., Fac.of Sci., Assoc. Prof., 理学部, 助教授 (60240727)
JIMBO Michio The Univ.of Tokyo, Graduate School of Math.Sci., Professor, 大学院・数理科学研究科, 教授 (80109082)
KONNO Hitoshi Hiroshima University, Fac.of Integrated Arts and Sciences, Assoc.Prof., 総合科学部, 助教授 (00291477)
KUMAHARA Keisaku The University of the Air, Fac.of Liberal Arts, Professor, 教養学部, 教授 (60029486)
MORITA Yoshiyuki Hiroshima University, Graduate School of Sci., Research Associate, 大学院・理学研究科, 助手 (20243545)
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| Research Abstract |
1. The Drinfeld realization of the face type eillptic quantum group B_<q,λ>(g)
In the cases g = A^<(1)>_n, A^<(2)>_2, we have realized the L-operator of the face type elliptic quantum group B_<q,λ>(g) in terms of the currents of the elliptic algebra U_<q,p>(g), which is an elliptic deformation of the Drinfeld currents of the affine quantum group U_q(g). Then we have shown the isomorphism U_<q,p>(g) 〓 B_<q,λ>(g) 【cross product】 C{H^^^} as an associative algebra. Here C{H^^^} is a Heisenberg algebra generated mainly by the pair of generators {P_j, Q_j} (j = 1, 【triple bond】, rank g)
2. wee field realization of U_<q,p>(g) and algebraic analysis of the solvable lattice models
The above isomorphism allows us to construct a free field realization of B_<q,λ>(g). For g = A^<(1)>_n, A^<(2)>_2, we lave constructed the level 1 free field realization of U_<q,p>(g), and obtained a realization of both the finite and infinite dimensional highest weight modules of U_<q,p>(g) and the vertex operator of U_<q,p>(g). These vertex operators are the U_<q,p>(g) counterpart of the B_<q,λ>(g)-intertwining operators. We also have identified the spaces of states in the A^<(1)>_n -type and A^<(2)>_2-type RSOS models with the U_<q,p>(g)-modules. The lance vertex operators in these RSOS models have also been identified with the vertex operators of corresponding U_<q,p>(g)
3. Relationship between B_<q,λ>(<sl>^^^^_n) and the deformed W_n-algebra
Extending the known relationship between the vertex operators of U_<q,p>(g) for g = A^<(1)>_1, A^<(2)>_2 acid the generating functions of the deformed W(g^^-)-algebras (deformed Virasoro algebra, in these cases), to the higher rank case p = A^<(1)>_<n-1>, we derived the generating functions of the deformed W_n-algebras by calculating the fusion of the level 1 vertex operators of U_<q,p>(<sl>^^^^_n)
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