拟三角形WZW模型的$q\to \infty$极限
$q\to \infty$ limit of the quasitriangular WZW model
摘要：
本文研究了WZW模型在单连通和单连通目标李群上的$q$ -形变的$q\to\infty$极限。证明了$q\to\infty$当前代数的对易关系是由从圆盘到目标群复化的全纯映射群上的仿射Poisson结构所决定的.对应于这种仿射泊松结构的李代数胚可以被积分为一个全局辛广群，这个全局辛广群只是$q$ -WZW模型的$q\to\infty$极限的相空间。我们还表明，这个辛grupoid承认手征分解兼容其（异常）Poisson-Lie对称性。最后，我们对偶的手征理论在一个显着的方式，我们评估的交换关系的$q\to\infty$手征WZW领域的原始和对偶图片。
英文摘要：
We study the $q\to\infty$ limit of the $q$-deformation of the WZW model on a compact simple and simply connected target Lie group. We show that the commutation relations of the $q\to\infty$ current algebra are underlied by certain affine Poisson structure on the group of holomorphic maps from the disc into the complexification of the target group. The Lie algebroid corresponding to this affine Poisson structure can be integrated to a global symplectic groupoid which turns out to be nothing but the phase space of the $q\to\infty$ limit of the $q$-WZW model. We also show that this symplectic grupoid admits a chiral decomposition compatible with its (anomalous) Poisson-Lie symmetries. Finally, we dualize the chiral theory in a remarkable way and we evaluate the exchange relations for the $q\to\infty$ chiral WZW fields in both the original and the dual pictures.
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