## Electronic Theses and Dissertations

Summer 2014

#### Degree Name

Master of Science in Mathematics (M.S.)

#### Document Type and Release Option

Thesis (open access)

#### Department

Department of Mathematical Sciences

Yi Lin

Francois Ziegler

Jimmy Dillies

#### Abstract

The Borel-Weil theorem is usually understood as a realization theorem for representations that have already been shown to exist by other means (Theorem of the Highest Weight''). In this thesis we turn the tables and show that, at least in the case of the classical groups $G = U(n)$, $SO(n)$ and $Sp(2n)$, the Borel-Weil construction can be used to quite explicitly prove existence of an irreducible representation having highest weight $\lambda$, for each dominant integral form $\lambda$ on the Lie algebra of a maximal torus of $G$.

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