本项目主要研究与Yokonuma-Hecke代数紧密相关的几类代数的结构和表示理论。整个课题共分为四部分，第一部分尝试发展任一交换Noether环上的仿射最高权范畴和仿射拟遗传覆盖理论；第二、四部分尝试构造仿射Yokonuma-Schur代数以及仿射和分圆YBMW代数，并且研究这几类代数的结构和不可约表示的分类；第三部分拟研究YBMW代数的结构和不可约表示的分类。本项目的关键研究手段为Hecke代数及相关代数的系统理论、表示论中的组合方法和（仿射）胞腔代数的方法，目标是得到某些重要类型的有限和无限维代数的结构和不可约表示的分类。这将有助于丰富和发展Hecke代数及其相关代数的结构和表示理论以及在其它相关数学领域的应用。

The present project is devoted to the structure and representation theory of several classes of algebras which are closely related to Yokonuma-Hecke algebras. It consists of four parts. In the first part, we shall develop the theory of affine highest weight categories and affine quasihereditary covers over a commutative noetherian ring. In the second and fourth part, we shall try to construct affine Yokonuma-Schur algebras, affine and cyclotomic YBMW algebras, and also consider the structure and classifications of irreducible representations of these algebras. In the third part, we shall consider the structure and classifications of irreducible representations of YBMW algebras. The main idea of our study is based on the systematic theory of Hecke algebras and related algebras, the combinatorial methods and the methods of (affine) cellular algebras. The main aim of the project is to obtain the structure and classifications of irreducible representations of some important types of finite and infinite dimensional algebras. This will help to enrich and develop the structure and representation theory of Hecke algebras and related algebras and its application in other related areas of mathematics.