多重基分拆与character公式
Multi-grounded partitions and character formulas
摘要：
我们介绍了一个新的推广分区，多接地分区，有关的基态路径索引的主导权的李代数。我们利用这些特征将仿射型Kac-Moody代数的不可约最高权模的特征标表示为多基划分的生成函数。这概括了我们以前的文件，其中只有不可约的最高权模块与恒定的基态路径被认为是所有的基态路径的方法。作为应用，我们计算了仿射李代数$A_{2n}^{(2)}(n\geq 2)$，$D_{n+1}^{(2)}(n\geq 2)$，$A_{2n-1}^{(1)}(n\geq 3)$，$B_{n}^{(1)}(n\geq 3)$，$D_{n}^{(1)}(n\geq 4)$的水平$1$模的特征.
英文摘要：
We introduce a new generalisation of partitions, multi-grounded partitions, related to ground state paths indexed by dominant weights of Lie algebras. We use these to express characters of irreducible highest weight modules of Kac-Moody algebras of affine type as generating functions for multi-grounded partitions. This generalises the approach of our previous paper, where only irreducible highest weight modules with constant ground state paths were considered, to all ground state paths. As an application, we compute the characters of the level $1$ modules of the affine Lie algebras $A_{2n}^{(2)}(n\geq 2)$, $D_{n+1}^{(2)}(n\geq 2)$, $A_{2n-1}^{(1)}(n\geq 3)$, $B_{n}^{(1)}(n\geq 3)$, and $D_{n}^{(1)}(n\geq 4)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
