The Spin Representation of the Symmetric Group

Abstract

Let Γn be the representation group or spin group (9; 4) of the symmetric group Sn. Then the irreducible representations of Γn can be allocated into two classes which we shall call (i) ordinary representations, which are the irreducible representations of the symmetric group, and (ii) spin or projective representations.As is well known (3; 5), there is an ordinary irreducible representation [λ] corresponding to every partition (λ) = (λ1, λ2, . . . , λm) of n withλ1 ≥ λ2 ≥ . . . ≥ λm > 0.