# Projective representation theory of alternating group:A4

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This article gives specific information, namely, projective representation theory, about a particular group, namely: alternating group:A4.
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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)).

Representation Degree Corresponding element of Schur multiplier, which is cyclic group:Z2 Number of ordinary representations of special linear group:SL(2,3) that give rise to it List of these (see linear representation theory of special linear group:SL(2,3))
trivial 1 trivial (identity element) 3 all the one-dimensional representations
three-dimensional 3 trivial (identity element) 1 the unique three-dimensional representation
two-dimensional 2 nontrivial (non-identity element) 3 all the two-dimensional representations

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.