COINVARIANTS IN CONFORMAL FIELDTHEORY

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We investigated the conformal coinvariants and its application to integrable quantum field theory.(i)The conformal coinvariants associated with integrable highest weight representations of affine Lie algebras have a natural filtration. We proved that they are isomorphic as filtered space to the space of coinvariants of the fusion products of finite dimensional modules in the sense of Feigin-Loktev. In some simple cases we also obtained explicit character formulas for the characters in terms of the restricted Kostka polynomials.(ii)We studied a family of symmetric polynomials satisfying certain zero conditions on the (shifted) diagonals. We showed that the ideal spanned by them has a basis in terms of a family of Macdonald polynomials at specific values of parameters q, t (q^<r-1>t^<k+1>=1).(iii)We studied the space of local fields in integrable quantum field theory, in the framework of the form factor bootstrap approach. Using their integral representations, each local, field is specified by an infinite series of polynomials which appear as integrand. In the case of the SU(2)-invariant Thirring model, we introduced an action of the quantum affine algebra U_√<-1>(<sl_2>^^^^) in the space of such sequences of polynomials, and proved that this space is isomorphic to the tensor product of the level 1 highest and level -1 lowest modules.