Representation of classical and quantum groups

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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.