Fermionic formulae originate in the Bethe ansatz in solvable lattice models. They are specific expressions of some q-polynomials as sums of products of q-binomial coefficients. We consider the… Expand

We introduce a fermionic formula associated with any quantum affine algebra U q (X N (r) . Guided by the interplay between corner transfer matrix and the Bethe ansatz in solvable lattice models, we… Expand

A series of solvable lattice models with face interaction are introduced on the basis of the affine Lie algebraXn(1)=An(1),Bn(1),Cn(1),Dn(1). The local states taken on by the fluctuation variables… Expand

A higher spin analogue is presented of the eight vertex-SOS correspondence in the sense of Andrews-Baxter-Forrester. The resulting hierarchy of solvable models contain the hard hexagon model and its… Expand

The box ball system is studied in the crystal theory formulation. New conserved quantities and the phase shift of the soliton scattering are obtained by considering the energy function (or H… Expand

A new hierarchy of solvable IRF models is presented. It is generated from Belavin's Zn×Znsymmetric model. The site variables take values in the set of level l dominant integral weights of A−1(1). It… Expand

Theq-deformed vertex operators of Frenkel and Reshetikhin are studied in the framework of Kashiwara's crystal base theory. It is shown that the vertex operators preserve the crystal structure, and… Expand