The Spin Representation of the Symmetric Group

Let Γnbe therepresentation group or spin group(9; 4) of the symmetric groupSn. Then the irreducible representations of Γncan be allocated into two classes which we shall call (i) ordinary representations, which are the irreducible representations of the symmetric group, and (ii)spinorprojectiverepresentations. As is well known (3; 5), there is an ordinary irreducible representation [λ] corresponding to every partition (λ) = (λ1, λ2, . . . , λm) ofnwith λ1≥ λ2≥ . . . ≥ λm> 0.