Crystalizing the Spinon Basis

The quasi-particle structure of the higher spin XXZ model is studied. We obtained a new description of crystals associated with the level k integrable highest weight Uq(ŝl2) modules in terms of the creation operators at q = 0 (the crystaline spinon basis). The fermionic character formulas and the Yangian structure of those integrable modules naturally follow from this description. We have also derived the conjectural formulas for the multi quasi-particle states at q = 0. Introduction In this paper, we consider the integrable XXZ spin chain with spin k/2 of sl2. The space of states is the infinit tensor product (the space of local fields) W = · · · ⊗C ⊗C ⊗C ⊗C ⊗ · · · . In remarkable papers [7, 25], using the Bethe Ansatz, Fadeev and Takhatajan discovered that the one-particle excitation in the anti-ferromagnetic regime of XXX chain is always (a kink of) spin 1/2. According to this picture, one can expect another description of space of states[7, 23] such as (the space of asymptotic particles)