Date Thesis Awarded
Bachelors of Science (BS)
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.
Cardin, Emilee, "Rankin-Cohen Brackets and Fusion Rules for Discrete Series Representations of SL(2,R)" (2019). Undergraduate Honors Theses. Paper 1394.