Representation of classical and quantum groups

对称性是自然而然存在的，许多科学家，包括数学家、化学家和物理学家，都对对称性感兴趣。通过把一个代数结构放在一个对象的对称集合上，就可以得到一个群。表示是一种将特定组与另一组进行标识的方式，该另一组具有允许提取关于原始组的信息的属性。许多表示法本质上是复杂的，人们希望找到研究它们的简化方法。这一建议涉及使用其他数学对象来研究特定群的表示，例如舒尔代数，这些对象允许人们发现关于原始表示的信息。

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.