Graded Hecke algebras and quasihereditary covers

我们研究了称为箭图Hecke代数的分次Hecke代数的表示理论。引入箭图Hecke代数是为了对量子群上的可积模进行分类。在研究的早期阶段，我们证明了某些非负性结果，这是谈到Fock空间范畴时必须保持的一个性质。在此之后，我们集中讨论了仿射型量子群上的基本模的分类。我们只能在很长一段时间内处理仿射类型A。在目前的研究中，我们已经成功地处理了仿射类型A以外的其他仿射类型，并证明了有限箭图Hecke代数的Erdmann-Nakano类型定理。特别地，它使我们能够详细地分析Tame表示型的有限箭图Hecke代数。与此相关，我们对两点对称特殊双列代数进行了分类。

We studied representation theory of graded Hecke algebras which are called quiver Hecke algebras. The quiver Hecke algebras were introduced for the purpose of categorifying integrable modules over quantum groups. In the early stage of the research, we proved certain nonnegativity result which was a property necessary to hold when we speak of categorification of Fock spaces. After that stage, we focused on categorification of basic modules over quantum groups of affine type. We were only able to handle the affine type A for long time. In the current research, we have succeeded in handling other affine types than affine type A and we have proved Erdmann-Nakano type theorems for finite quiver Hecke algebras. In particular, it allowed us to analyze finite quiver Hecke algebras of tame representation type in detail. Related to this analysis, we have classified two point symmetric special biserial algebras.