Notes on $\widetilde{\mathrm{SL}}(2,\mathbb{R})$ representations

TL;DR

This paper explores representations of the universal cover of SL(2,R), focusing on their applications in physics, including spinors on hyperbolic and anti-de Sitter spaces.

Contribution

It provides a detailed analysis of SL(2,R) representations and their relevance to physical models involving hyperbolic geometry and anti-de Sitter space.

Findings

Characterization of universal cover representations

Connection to spinor fields on hyperbolic space

Implications for physics in anti-de Sitter space

Abstract

These notes describe representations of the universal cover of $\mathrm{SL}(2,\mathbb{R})$ with a view toward applications in physics. Spinors on the hyperbolic plane and the two-dimensional anti-de Sitter space are also discussed.