Linear representation theory of special linear group:SL(2,9)

GAP implementation
The degrees of irreducible representations can be computed using CharacterDegrees as follows:

gap> CharacterDegrees(SL(2,9)); [ [ 1, 1 ], [ 4, 2 ], [ 5, 2 ], [ 8, 4 ], [ 9, 1 ], [ 10, 3 ] ]

This says that there is 1 irreducible representation of degree 1, 2 of degree 4, 2 of degree 5, 4 of degree 8, 1 of degree 9, and 3 of degree 10.

The character table can be computed using the Irr and CharacterTable functions as follows:

gap> Irr(CharacterTable(SL(2,9))); [ Character( CharacterTable( SL(2,9) ), [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,     1, 1 ] ), Character( CharacterTable( SL(2,9) ),    [ 4, 2, -1, -4, -2, 1, -1, -1, 1, 1, 0, 0, 0 ] ), Character( CharacterTable( SL(2,9) ), [ 4, -1, 2, -4, 1, -2, -1, -1, 1, 1,     0, 0, 0 ] ), Character( CharacterTable( SL(2,9) ),    [ 5, 2, -1, 5, 2, -1, 0, 0, 0, 0, -1, 1, -1 ] ), Character( CharacterTable( SL(2,9) ), [ 5, -1, 2, 5, -1, 2, 0, 0, 0, 0,     -1, 1, -1 ] ), Character( CharacterTable( SL(2,9) ),    [ 8, 1, 1, -8, -1, -1, -E(5)-E(5)^4, -E(5)^2-E(5)^3, E(5)+E(5)^4,      E(5)^2+E(5)^3, 0, 0, 0 ] ), Character( CharacterTable( SL(2,9) ),    [ 8, 1, 1, -8, -1, -1, -E(5)^2-E(5)^3, -E(5)-E(5)^4, E(5)^2+E(5)^3,      E(5)+E(5)^4, 0, 0, 0 ] ), Character( CharacterTable( SL(2,9) ),    [ 8, -1, -1, 8, -1, -1, -E(5)^2-E(5)^3, -E(5)-E(5)^4, -E(5)^2-E(5)^3,      -E(5)-E(5)^4, 0, 0, 0 ] ), Character( CharacterTable( SL(2,9) ),    [ 8, -1, -1, 8, -1, -1, -E(5)-E(5)^4, -E(5)^2-E(5)^3, -E(5)-E(5)^4,      -E(5)^2-E(5)^3, 0, 0, 0 ] ), Character( CharacterTable( SL(2,9) ),    [ 9, 0, 0, 9, 0, 0, -1, -1, -1, -1, 1, 1, 1 ] ), Character( CharacterTable( SL(2,9) ), [ 10, 1, 1, 10, 1, 1, 0, 0, 0, 0, 0,     -2, 0 ] ), Character( CharacterTable( SL(2,9) ),    [ 10, -1, -1, -10, 1, 1, 0, 0, 0, 0, -E(8)+E(8)^3, 0, E(8)-E(8)^3 ] ), Character( CharacterTable( SL(2,9) ), [ 10, -1, -1, -10, 1, 1, 0, 0, 0, 0,     E(8)-E(8)^3, 0, -E(8)+E(8)^3 ] ) ]

The irreducible representations can be computed using the IrreducibleRepresentations function as follows:

gap> IrreducibleRepresentations(SL(2,9));