Lindsay Skinner

Groups are abstract mathematical structures that are fundamental to nearlyall branches of abstract algebra. Representation theory gives us the tools tostudy groups using concrete matrices. For this reason representation theoryis a powerful tool, but finding representations is not an easy task. In thistalk we shall explore some of the fundamentals of representation theory.We will use this foundation to show that the set of degreedpolynomials intwo variables is an irreducible GL2 module. This result can then begeneralized to our main theorem, which constructs a large class ofirreducible representations of the general linear group.