JIMBO Michio Hiroshima Univ., Graduate school of Math., Prof., 大学院・数理科学研究科, 教授 (80109082)
TANISAKI Toshiyuki Hiroshima Univ., Graduate school of Sci., Prof., 大学院・理学研究科, 教授 (70142916)
EGUCHI Masaaki Hiroshima Univ., Fac. of Integrated Arts & Sci., Prof., 総合科学部, 教授 (30037220)
TAKEBE Takashi Ochanomizu Univ., Dept. of Math., Assoc. Prof., 理学部, 助教授 (60240727)
1. Formulation of the ABF model in regime II in terms of the vertex operators
Supposing the local height restriction is κ + 1, we have identified the half-infinite row and column transfer matrices and the creation operator of the physical excitation with the vertex operators and the basic q-parafermion currents of the q-deformed Ζ_κ parafermion theory, respectively. We have also shown that the scaling limit of the model is given by Koberle-Swieca's factorized scattering theory.
2. Representation of <sl>^^^^_2 in the principal gradation
We have given a free field realization of the representation of <sl>^^^^_2 in the generic level principal gradation. Especially, we have given a free field realization of Lepowsky-Wilson's Ζ-algebra as the deformed Virasoro algebra Vir_<q, t> in the limit (t = -q^<(k+22)/2>, q → 1).
3. Higher level representation of the elliptic quantum group β_<q,【lambda bar】>(<sl>^^^^_2)
Based on the free field realization of β_<q,【lambda bar】>(<sl>^^^^_2) and the elliptic algebra U_<q, p>(<sl>^^^^_2), we have given a systematic construction of the higher spin intertwining operators of β_<q,【lambda bar】>(<sl>^^^^_2). We have also clarified a relation between the coset decomposition of the tensor product of two U_q(<sl>^^^^_2)-modules and the representation of U_<q, p>(<sl>^^^^_2).