AI 中文总结
本文研究对应等秩实群的秩2 Lusztig-Vogan范畴，分类其不可分解对象、刻画生成Soergel双模的作用，还提供适用于任意有限秩该范畴的算法，复现了对应Lusztig-Vogan模的W-图。
AI 中文摘要
Lusztig-Vogan范畴是Hecke代数上Lusztig-Vogan模主块的范畴化，其可捕获实约化群不可约容许表示的特征信息，可构造为Soergel双模的模范畴。本文描述对应等秩实群的秩2 Lusztig-Vogan范畴的结构，具体对不可分解对象进行分类，刻画生成Soergel双模的作用，复现基础Lusztig-Vogan模的W-图；还提供了一种算法，可对任意有限秩Lusztig-Vogan范畴完成该过程，包括那些不对应实约化群的范畴。
英文摘要
Lusztig-Vogan categories are categorifications of the principal block of the Lusztig-Vogan module over the Hecke algebra, which captures information about characters of irreducible admissible representations of a real reductive group. Lusztig-Vogan categories can be constructed as module categories over Soergel bimodules. In this paper, we describe the structure of the rank 2 Lusztig-Vogan categories corresponding to equal rank real groups. More precisely, we classify indecomposable objects and describe the action of generating Soergel bimodules, recovering the $W$-graph of the underlying Lusztig-Vogan module. We also provide an algorithm which completes this procedure for arbitrary finite rank Lusztig-Vogan categories, including those which do not correspond to a real reductive group.
Comments32 pages, 8 figures, comments welcome
