论文标题
$ \ Mathbf {B} _2^{（1）} $ affine toda系统的爆炸分析
The Blow-up Analysis on $\mathbf{B}_2^{(1)}$ Affine Toda system: Local mass and Affine Weyl group
论文作者
论文摘要
已经确定，与简单的Lie代数$ \ MATHBF {A} _n，〜\ \ \ Mathbf {B} _N，〜\ Mathbf {C} _n $和$ \ Mathbf {G} _2 $可以由Pinite weyl组来代表您。特别是，在每个爆炸点进行一系列起泡步骤（通过缩放）后，每个步骤的局部质量的转换对应于Weyl组中元素的作用。在本文中，我们以相同的精神介绍了仿射$ \ mathbf {b} _2^{（1）} $ toda系统具有奇异性。与具有简单的Lie代数的TODA系统相比，由于{offine weyl of type $ \ mathbf {b} _ {2} _ {2}^{（1）} $} {offine weyl off offinite的计算局部质量的计算更具挑战性。为了给出当地质量公式的明确表达，我们介绍了两个免费整数，并将所有可能性写入8种类型。这显示了与简单的Lie代数的TODA系统的先前结果显着的差异。本文的主要结果似乎是理解主张TODA系统的爆炸分析与相关谎言代数的{offine weyl grout}之间的关系的第一个主要进步。
It has been established that the local mass of blow-up solutions to Toda systems associated with the simple Lie algebras $\mathbf{A}_n,~\mathbf{B}_n,~\mathbf{C}_n$ and $\mathbf{G}_2$ can be represented by a finite Weyl group. In particular, at each blow-up point, after a sequence of bubbling steps (via scaling) is performed, the transformation of the local mass at each step corresponds to the action of an element in the Weyl group. In this article, we present the results in the same spirit for the affine $\mathbf{B}_2^{(1)}$ Toda system with singularities. Compared with the Toda system with simple Lie algebras, the computation of local masses is more challenging due to the infinite number of elements of the {affine Weyl group of type $\mathbf{B}_{2}^{(1)}$}. In order to give an explicit expression for the local mass formula we introduce two free integers and write down all the possibilities into 8 types. This shows a striking difference to previous results on Toda systems with simple Lie algebras. The main result of this article seems to provide the first major advance in understanding the relation between the blow-up analysis of affine Toda system and the {affine Weyl group} of the associated Lie algebras.
