Thumbnail Image
Item

Rankin-Cohen Brackets and Fusion Rules for Discrete Series Representations of SL(2,R)

Cardin, Emilee
Abstract
In this paper, we discuss the holomorphic discrete series representations of SL(2,R). We give an overview of general representation theory, from the perspective of both groups and Lie algebras. We then consider tensor products of representations, specifically investigating tensor products of the holomorphic discrete series and their associated algebraic objects, called (g,K)-modules. We then use algebraic techniques to study the fusion rules of the discrete series. We conclude by giving explicit intertwiners, recovering the formula of number-theoretic objects, called Rankin-Cohen brackets.
Description
Date
2019-04-01
Journal Title
Journal ISSN
Volume Title
Publisher
Collections
Undergraduate Honors Theses
Show all metadata
Download Dataset
Files
CompletedThesis.pdf
Adobe PDF, 325.93 KB
Rights Holder
Usage License
Embargo
Research Projects
Organizational Units
Journal Issue
Keywords
Citation
Advisor
Clare, Pierre
Vinroot, Ryan
Ekstrom, Laura
Department
Mathematics
DOI
URI
https://scholarworks.wm.edu/handle/internal/10794
Embedded videos