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