COINVARIANTS IN CONFORMAL FIELDTHEORY

研究了共形协不变量及其在可积量子场论中的应用：(I)仿射李代数的可积最高权表示所对应的共形协不变量具有自然滤子。证明了它们与有限维模在Feigin-Loktev意义下的融合积的余不变量空间同构为滤子空间。在一些简单的情况下，我们还得到了用限制Kostka多项式表示的特征标的显式特征标公式。(Ii)我们研究了一族对称多项式，它满足(移位)对角线上的某些零条件。我们证明了在参数q，t(q^&lt；r-1&gt；t^&lt；k+1&gt；=1)的特定值下，它们所跨越的理想具有一族Macdonald多项式的基。(Iii)在形式因子Bootstrap方法的框架下，我们研究了可积量子场论中的局域场空间。使用它们的积分表示法，每个局部场由一个看起来像被积函数的无穷级数多项式来指定。在SU(2)-不变Thirring模型的情形下，我们引入了量子仿射代数U_√&lt；-1&gt；(&lt；sl_2&gt；^)在这类多项式序列空间中的作用，并证明了这个空间同构于1级最高模和1级最低模的张量积。

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.