A Constructive Proof of the Borel-Weil Theorem for Classical Groups

<p>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 $G$.</p>

Name thesis:degree_name

Master of Science in Mathematics (M.S.)

Level thesis:degree_level

Thesis (open access)

Discipline thesis:degree_discipline

Department of Mathematical Sciences

Year dc:date.available

2014

Author dc:creator

• Timchenko, Kostiantyn

Contributors dc:contributor

• Francois Ziegler
• Jimmy Dillies

• ETD
• Unitary representation
• coadjoint orbit
• geometric quantization
• Kahler manifold
• Geometry and Topology
• Mathematics

Repository record dc:identifier

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

OAI identifier oai:identifier

oai:digitalcommons.georgiasouthern.edu:etd-2206