论文标题
$ 1 $ $ c_n^{（1）} $的字符$ 1 $标准模块作为通用分区的生成函数
Characters of level $1$ standard modules of $C_n^{(1)}$ as generating functions for generalised partitions
论文作者
论文摘要
我们给出了一个新的简单公式，用于$ 1 $ 1 $ $ c_n^{（1）} $的能量功能，由Kang，Kashiwara和Misra引入。我们使用它来为$ 1 $标准模块的字符提供多个表达式，作为为不同类型的分区生成功能。然后，我们将这些公式之一与Capparelli，Meurman，Primc和Primc的猜想分区身份的差异条件联系起来，并证明它们的猜想在所有级别的$ 1 $标准模块中都是正确的。最后，我们提出了对其猜想的非专业概括。
We give a new simple formula for the energy function of a level $1$ perfect crystal of type $C_n^{(1)}$ introduced by Kang, Kashiwara and Misra. We use this to give several expressions for the characters of level $1$ standard modules as generating functions for different types of partitions. We then relate one of these formulas to the difference conditions in the conjectural partition identity of Capparelli, Meurman, Primc and Primc, and prove that their conjecture is true for all level $1$ standard modules. Finally, we propose a non-specialised generalisation of their conjecture.
