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Minimal Principal Series Representations of SL(3,R)

Gliozzi, Jacopo
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.
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2019-05-01
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Undergraduate Honors Theses
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Clare, Pierre
Li, Chi-Kwong
Rossi, Enrico
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Mathematics
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https://scholarworks.wm.edu/handle/internal/10699
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