Solvable Lattice Models and Elliptic Quantum Groups

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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.