Realising the projective representations of the symmetric group using Dirac cohomology.

Firstly I will outline Dirac cohomology for graded Hecke algebras and the branching rules for the projective representations of $S_n$. Combining these notions with the Jucys-Murphy elements for $\tilde{S}_n$, that is the double cover of the symmetric group, I will go through a method to completely describe the spectrum data for the Jucys-Murphy elements for $\tilde{S}_n$. If time allows I will also explain how this spectrum data gives rise to a a concrete description for the matrices of the action of $\tilde{S}_n$.