COINVARIANTS IN CONFORMAL FIELDTHEORY

研究了共形协变量及其在可积量子场论中的应用。(1)仿射李代数的可积最高权表示的共形协不变量具有自然滤除性。在Feigin-Loktev意义下证明了它们作为滤波空间与有限维模的融合积的协变量空间是同构的。在一些简单的情况下，我们也得到了用受限Kostka多项式表示的字符的显式字符公式。（ii）研究了在移位对角线上满足一定零条件的对称多项式族。我们证明了由它们张成的理想在特定参数q， t的值上具有麦克唐纳多项式族的基（q^<r-1>t^<k+1>=1）。（iii）在形式因子自举方法的框架下，研究了可积量子场论中的局部场空间。利用它们的积分表示，每个局部域都由无穷级数的多项式来表示，这些多项式表现为被积数。对于SU(2)-不变Thirring模型，我们引入了量子仿射代数U_√<-1>(<sl_2>^^^^)在该多项式序列空间中的作用，并证明了该空间与1级最高和1级最低模的张量积同构。

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.