The Spin Representation of the Symmetric Group

Abstract

Let Γ n be the representation group or spin group (9; 4) of the symmetric group Sn . Then the irreducible representations of Γ n 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, . . . , λ m ) of n with λ1 ≥ λ2 ≥ . . . ≥ λ m > 0.