# Linear representation theory of double cover of symmetric group

Note that for every $n \ge 4$, there are two different double covers $2 \cdot S_n^-$ and $2 \cdot S_n^+$. However, both of them have the same degrees of irreducible representations, though the actual set of irreducible representations depends on the group.
$n$ $2(n!)$ (order of $2 \cdot S_n^-$ and $2 \cdot S_n^+$ $2 \cdot S_n^-$ $2 \cdot S_n^+$ number of irreducible representations (= number of conjugacy classes) degrees of irreducible representations number of irreducible representations of $S_n$ (correspond to irreducible representations of either double cover that have the center in the kernel) degrees of these irreducible representations number of irreducible representations of the double cover that do not have the center in their kernel degrees of these irreducible representations linear representation theory information on $2 \cdot S_n^-$ linear representation theory information on $2 \cdot S_n^+$