Highest weight representations of the N=1 Ramond algebra

We analyze the highest weight representations of the N=1 Ramond algebra using ordering properties of the algebra. In particular we obtain ordering kernel expressions for all (primitive) N=1 Ramond singular vectors. After choosing a suitable ordering for the N=1 Ramond algebra generators we compute the ordering kernel, which turns out to be two-dimensional for complete Verma modules and one-dimensional for G-closed Verma modules. These two-dimensional ordering kernels allow us to derive multiplication rules for singular vector operators and lead to expressions for degenerate singular vectors. Using these multiplication rules we study descendant singular vectors and derive the Ramond embedding diagrams for the rational models. We explain their differences to embedding diagrams previously suggested in the literature. Our method also confirms the recent findings by Iohara and Koga that certain Verma modules over the N=1 Ramond algebra contain degenerate (2-dimensional) singular vector spaces and that for Verma modules with conformal weight Δ=c/24 (Verma modules with Ramond ground states) the modules can even contain subsingular vectors. We give all explicit examples for singular vectors, degenerate singular vectors, and subsingular vectors until level 3.