Representation of classical and quantum groups

对称性在世界上自然存在，许多科学家包括数学家、化学家和物理学家都对此感兴趣。把一个代数结构放在一个物体的对称集合上，就得到一个群。表示是一种将特定组与另一组识别的方法，该组具有允许提取有关原始组的信息的属性。许多表示本质上是复杂的，需要找到简化的方法来研究它们。这一建议涉及到使用其他数学对象（如舒尔代数）来研究特定群体的表示，这些数学对象允许人们发现有关原始表示的信息。

Symmetries occur naturally in the world and are of interest to many scientists including mathematicians, chemists, and physicists. By placing an algebraic structure on the set of symmetries of an object, one obtains a group. A representation is a way of identifying a particular group with another group that has properties which allow one to extract information about the original group. Many representations are intrinsically complicated and it is desirable to find simplified methods for studying them. This proposal is concerned with the study of representations for particular groups using other mathematical objects such as Schur algebras that allow one to discover information about the original representation.