Date Thesis Awarded

4-2019

Document Type

Honors Thesis

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Pierre Clare

Committee Members

Ryan Vinroot

Laura Ekstrom

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.

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