论文标题
Hernandez-leclerc类别中的主要表示：经典分解
Prime representations in the Hernandez-Leclerc category: classical decompositions
论文作者
论文摘要
我们使用循环代数的双重功能实现来研究与$ \ mathfrak {sl} _ {n+1} $相关的量子仿射代数的hernandez-leclerc类别中的主要不可还原对象。当HL类别被实现为群集代数\ cite {hl10，hl13}的单体分类时，这些表示完全对应于群集变量，而冷冻变量是最小的关联。对于任何高度函数，我们确定这些表示相对于Hopf subsalgebra $ \ Mathbf {u} _q（\ Mathfrak {sl} _ {n+1}）$的经典分解，并描述其分级的层次多重性的分级多重性。结合\ cite {bcmo15}，我们在相应的仿射元素代数的两个级别的两个可集成的最高权重表示中获得了稳定的质量启动模块的分级分解。
We use the dual functional realization of loop algebras to study the prime irreducible objects in the Hernandez-Leclerc category for the quantum affine algebra associated to $\mathfrak{sl}_{n+1}$. When the HL category is realized as a monoidal categorification of a cluster algebra \cite{HL10,HL13}, these representations correspond precisely to the cluster variables and the frozen variables are minimal affinizations. For any height function, we determine the classical decomposition of these representations with respect to the Hopf subalgebra $\mathbf{U}_q(\mathfrak{sl}_{n+1})$ and describe the graded multiplicities of their graded limits in terms of lattice points of convex polytopes. Combined with \cite{BCMo15} we obtain the graded decomposition of stable prime Demazure modules in level two integrable highest weight representations of the corresponding affine Lie algebra.
