Factor-representations of the infinite spin-symmetric group

Let $S(\infty)$ be the group of finitary permutations of the sequence of natural numbers. The infinite spin-symmetric group is its central $\mathbb{Z}_2$-extension. This extension linearizes projective representations of the group $S(\infty)$. In this article factor-representations of $\mathrm{II}_1$-type of the group $T(\infty)$ are described.