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

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.