Summary: We derive an explicit description of the genuine projective representations of the symmetric group \(S_n\) using Dirac cohomology and the branching graph for the irreducible genuine projective representations of \(S_n\). D. Ciubotaru and X. He [Adv. Math. 283, 1–50 (2015; Zbl 1367.20037)], using the extended Dirac index, showed that the characters of the projective representations of \(S_n\) are related to the characters of elliptic-graded modules. We derive the branching graph using Dirac theory and combinatorics relating to the cohomology of Borel varieties \(\mathcal{B}_e\) of \(\mathfrak{g}\) and are able to use Dirac cohomology to construct an explicit model for the projective representations. We also describe Vogan’s morphism for Hecke algebras in type A using spectrum data of the Jucys-Murphy elements.