Matrix Elements and Characters of the Discrete Series ("Massive") Unitary Irreducible Representations of Sp(4,R)

TL;DR

This paper derives the matrix elements and characters of the discrete series unitary irreducible representations of Sp(4,R), which are crucial for understanding symmetries in anti-de Sitter spacetime.

Contribution

It provides explicit formulas for matrix elements and characters of the discrete series UIRs of Sp(4,R), advancing the mathematical understanding of this group's representations.

Findings

Explicit matrix elements derived for Sp(4,R) discrete series

Characters of the discrete series representations computed

Enhanced understanding of Sp(4,R) in anti-de Sitter physics

Abstract

This paper obtains the matrix elements and characters of the discrete series unitary irreducible representations (UIRs) of the Sp$(4,\mathbb{R})$ group. With an isomorphic relationship to the two-fold covering of SO$_0(2,3)$ (Sp$(4,\mathbb{R}) \sim$ SO$_0(2,3)\times \mathbb{Z}_2$), this group holds particular importance as the kinematical/relativity group within the framework of ($1+3$-dimensional) anti-de Sitter spacetime.