College of Graduate Studies: Theses & Dissertations
Term of Award
Summer 2014
Degree Name
Master of Science in Mathematics (M.S.)
Document Type and Release Option
Thesis (open access)
Copyright Statement / License for Reuse
Digital Commons@Georgia Southern License
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). College of Graduate Studies: Theses & Dissertations. 1144.
https://digitalcommons.georgiasouthern.edu/etd/1144
