Representations of Fuchsian Groups, Parahoric Group Schemes by Vikraman Balaji

Explore the intricate world of Fuchsian groups and parahoric group schemes in this comprehensive lecture from the International Centre for Theoretical Sciences. Delve into key concepts including principal G-bundles, root systems, Cartan matrices, and affine roots. Examine the properties of highest roots in G-simple groups and study the unique example of G2. Investigate root homomorphisms and parahoric groups before focusing on Fuchsian groups and their parabolic representations. Gain insights into advanced mathematical structures and their applications in geometry and topology through this in-depth presentation, complete with a Q&A session to reinforce understanding.

Representations of Fuchsian groups, parahoric group schemes
Outline
Principal G-bundle
Definition of Root System
Chambers of R
Highest Root: G-simple, the adjoint representation which is reducible has a unique highest weight
Cartan matrix
Affine roots
Basic affine roots
Note
Example G2
Root Homomorphisms
Basic example of the paregoric group
Fuchsian groups
First case-parabolic
Lemma
Q&A