论文标题
第二级的加权单词，II：平面分区，常规分区和应用一级完美晶体
Weighted words at degree two, II: flat partitions, regular partitions, and application to level one perfect crystals
论文作者
论文摘要
在最近的一项工作中，基思（Keith）和xiong通过使用Sylvester式的两次射击来对Glaisher定理进行了改进。在本文中，我们介绍了两个有色隔板的家族，平坦的和常规分区，并将基思和Xiong的两者概括为这些分区。然后，使用本系列的第一篇论文的结果，我们陈述了两个结果，其中第一个是一级上的结果，其中分区的零件具有原色的零件，第二级结果是二级彩色分区的第二个结果。这些结果使我们可以轻松检索$ a_ {2n}^{（2）}，d_ {n+1}^{（2）} $ a_ {2n}^{（2）} $ a_ {2n}^{（2）} $和$ b_n^{（1）} $的Frenkel-kac字符公式，以及在纸面上和表象中进行了陈述。
In a recent work, Keith and Xiong gave a refinement of Glaisher's theorem by using a Sylvester-style bijection. In this paper, we introduce two families of colored partitions, flat and regular partitions, and generalize the bijection of Keith and Xiong to these partitions. We then state two results, the first at degree one, where partitions have parts with primary colors, and the second result at degree two for secondary-colored partitions, using the result of the first paper of this series. These results allow us to easily retrieve the Frenkel-Kac character formulas of level one standard modules for the type $A_{2n}^{(2)}, D_{n+1}^{(2)}$ and $B_n^{(1)}$, and also to make the connection between the result stated in paper one and the representation theory.
