Projective representation theory of alternating group:A4

This article describes the projective linear representations of alternating group:A4.

The Schur multiplier of alternating group:A4 is cyclic group:Z2, and the corresponding Schur covering group is special linear group:SL(2,3). Thus, the projective representations of alternating group:A4 all arise from (ordinary) linear representations of special linear group:SL(2,3) (see linear representation theory of special linear group:SL(2,3)).

Note that a representation corresponding to the trivial element of the Schur multiplier is precisely a representation that descends to a linear representation of alternating group:A4.