COINVARIANTS IN CONFORMAL FIELDTHEORY

共形场理论中的协变量

• 批准号: 14340040
• 负责人: JIMBO Michio
• 金额: $ 3.39万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-14340040/
• 关键词: Conformal field theory; Coinvariants; Macdonald polynomials; form factors; Sine-Gordon model; quantum affine algebras; 量子群; フュージョン積; 指標; マクドナルド多項式; フェルミ型公式

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.

本文研究了共形共不变量及其在可积量子场论中的应用。（i）与仿射李代数的可积最高权表示相关联的共形共不变量具有自然滤子。证明了它们作为滤子空间同构于Feigin-Loktev意义下的有限维模的融合积的共不变量空间。在一些简单的情况下，我们还得到了特征标用限制Kostka多项式表示的显式特征标公式。（ii）研究了一类在（移位）对角线上满足一定零点条件的对称多项式。我们证明了它们所张成的理想在参数q，t（q^<r-1>t^&lt;k+1&gt;=1）的特定值下有一族Macdonald多项式的基.（iii）在形状因子自举方法的框架下，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，每个局部域由作为被积函数出现的多项式的无穷级数指定。在SU（2）不变的Thirring模型的情形下，我们引入了量子仿射代数U_∞<-1>（<sl_2>^）在这类多项式序列空间中的作用，并证明了这类空间同构于1阶最高模和-1阶最低模的张量积.

项目成果

M.Jimbo, T.Miwa, Y.Takeyarna: "Counting minimal form factors of the restricted sine-Gordon model."Moscow Math. J.. (in press).

M.Jimbo、T.Miwa、Y.Takearna：“计算受限正弦戈登模型的最小形状因数。”莫斯科数学。

B.Feigin, M.Jimbo, R.Kedem, S.Loktev, T.Miwa: "Spaces of coinvariants and fusion product I."Duke Math.. (in press).

B.Feigin、M.Jimbo、R.Kedem、S.Loktev、T.Miwa：“协变体和融合积 I 的空间”。Duke Math..（正在出版）。

B.Feigin et al.: "Symmetric polynomials vanishing on the Shifted diagonals and Macdonald polynomials"Int.Math.Res.Notices. 18. 1015-1034 (2003)

B.Feigin 等人：“对称多项式在平移对角线上消失和麦克唐纳多项式”Int.Math.Res.Notices。

M.Jimbo et al.: "Counting minimal form factors of the restricted sine-Gordon on model"Moscow Math.J.. (印刷中).

M. Jimbo 等人：“计算模型上受限正弦戈登的最小形状因数”Moscow Math.J.（正在出版）。

B.Feigin et al.: "Symmetric polynomials vanishing on the diagonals shifted by roots of unity"Int.Math.Res.Notice. 18. 999-1014 (2003)

B.Feigin 等人：“对称多项式在单位根移动的对角线上消失”Int.Math.Res.Notice。