Linear representation theory of alternating group:A9

Degrees of irreducible representations
These can be computed using the CharacterDegrees and CharacterTable functions:

gap> CharacterDegrees(CharacterTable(AlternatingGroup(9))); [ [ 1, 1 ], [ 8, 1 ], [ 21, 2 ], [ 27, 1 ], [ 28, 1 ], [ 35, 2 ], [ 42, 1 ], [ 48, 1 ], [ 56, 1 ], [ 84, 1 ], [ 105, 1 ], [ 120, 1 ], [ 162, 1 ], [ 168, 1 ], [ 189, 1 ], [ 216, 1 ] ]

Character table
These can be computed using the Irr and CharacterTable functions:

gap> Irr(CharacterTable(AlternatingGroup(9))); [ Character( CharacterTable( Alt( [ 1 .. 9 ] ) ),   [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] ), Character( CharacterTable( Alt( [ 1 .. 9 ] ) ),   [ 8, 4, 0, 5, 1, 2, -1, 2, -1, 0, 3, -1, 0, 0, 0, 1, -1, -1 ] ), Character( CharacterTable( Alt( [ 1 .. 9 ] ) ),   [ 21, 1, -3, -3, 1, 0, 3, -1, -1, 1, 1, 1,      -E(15)-E(15)^2-E(15)^4-E(15)^8, -E(15)^7-E(15)^11-E(15)^13-E(15)^14,      0, 0, 0, 0 ] ), Character( CharacterTable( Alt( [ 1 .. 9 ] ) ),    [ 21, 1, -3, -3, 1, 0, 3, -1, -1, 1, 1, 1,      -E(15)^7-E(15)^11-E(15)^13-E(15)^14, -E(15)-E(15)^2-E(15)^4-E(15)^8,      0, 0, 0, 0 ] ), Character( CharacterTable( Alt( [ 1 .. 9 ] ) ),    [ 27, 7, 3, 9, 1, 0, 0, 1, 1, -1, 2, 2, -1, -1, 0, -1, 0, 0 ] ), Character( CharacterTable( Alt( [ 1 .. 9 ] ) ),   [ 28, 4, -4, 10, -2, 1, 1, 0, 0, 0, 3, -1, 0, 0, -1, 0, 1, 1 ] ), Character( CharacterTable( Alt( [ 1 .. 9 ] ) ),   [ 35, -5, 3, 5, 1, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, -1, 2 ] ), Character( CharacterTable( Alt( [ 1 .. 9 ] ) ),   [ 35, -5, 3, 5, 1, 2, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 2, -1 ] ), Character( CharacterTable( Alt( [ 1 .. 9 ] ) ),   [ 42, 6, 2, 0, 0, 3, -3, 0, 0, 2, -3, 1, 0, 0, -1, 0, 0, 0 ] ), Character( CharacterTable( Alt( [ 1 .. 9 ] ) ),   [ 48, 8, 0, 6, 2, 0, 3, 0, 0, 0, -2, -2, 1, 1, 0, -1, 0, 0 ] ), Character( CharacterTable( Alt( [ 1 .. 9 ] ) ),   [ 56, -4, 0, 11, -1, 2, 2, -2, 1, 0, 1, 1, 1, 1, 0, 0, -1, -1 ] ), Character( CharacterTable( Alt( [ 1 .. 9 ] ) ),   [ 84, 4, 4, -6, -2, 3, 3, 0, 0, 0, -1, -1, -1, -1, 1, 0, 0, 0 ] ), Character( CharacterTable( Alt( [ 1 .. 9 ] ) ),   [ 105, 5, 1, 15, -1, -3, -3, -1, -1, 1, 0, 0, 0, 0, 1, 0, 0, 0 ] ), Character( CharacterTable( Alt( [ 1 .. 9 ] ) ),   [ 120, 0, 8, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0 ] ), Character( CharacterTable( Alt( [ 1 .. 9 ] ) ),   [ 162, 6, -6, 0, 0, 0, 0, 0, 0, -2, -3, 1, 0, 0, 0, 1, 0, 0 ] ), Character( CharacterTable( Alt( [ 1 .. 9 ] ) ),   [ 168, 4, 0, -15, 1, 0, -3, -2, 1, 0, 3, -1, 0, 0, 0, 0, 0, 0 ] ), Character( CharacterTable( Alt( [ 1 .. 9 ] ) ),   [ 189, -11, -3, 9, 1, 0, 0, 1, 1, 1, -1, -1, -1, -1, 0, 0, 0, 0 ] ), Character( CharacterTable( Alt( [ 1 .. 9 ] ) ),   [ 216, -4, 0, -9, -1, 0, 0, 2, -1, 0, 1, 1, 1, 1, 0, -1, 0, 0 ] ) ]