Projective representation theory of alternating group:A4
This article gives specific information, namely, projective representation theory, about a particular group, namely: alternating group:A4.
View projective representation theory of particular groups | View other specific information about 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.