#### Term of Award

Summer 2014

#### Degree Name

Master of Science in Mathematics (M.S.)

#### Document Type and Release Option

Thesis (open access)

#### Department

Department of Mathematical Sciences

#### Committee Chair

Yi Lin

#### Committee Member 1

Francois Ziegler

#### Committee Member 2

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 $G$.

#### Recommended Citation

Timchenko, Kostiantyn, "A Constructive Proof of the Borel-Weil Theorem for Classical Groups" (2014). *Electronic Theses & Dissertations*. 1144.

https://digitalcommons.georgiasouthern.edu/etd/1144