Date Thesis Awarded
5-2019
Access Type
Honors Thesis -- Access Restricted On-Campus Only
Degree Name
Bachelors of Science (BS)
Department
Mathematics
Advisor
Pierre Clare
Committee Members
Chi-Kwong Li
Enrico Rossi
Abstract
We discuss the properties of principal series representations of SL(3,R) induced from a minimal parabolic subgroup. We present the general theory of induced representations in the language of fiber bundles, and outline the construction of principal series from structure theory of semisimple Lie groups. For SL(3,R), we show the explicit realization a novel picture of principal series based on the nonstandard picture introduced by Kobayashi, Orsted, and Pevzner for symplectic groups. We conclude by studying the K-types of SL(3,R) through Frobenius reciprocity, and evaluate prospects in developing simple intertwiners between principal series representations.
Recommended Citation
Gliozzi, Jacopo, "Minimal Principal Series Representations of SL(3,R)" (2019). Undergraduate Honors Theses. William & Mary. Paper 1308.
https://scholarworks.wm.edu/honorstheses/1308
