Eigenvalues( tbl, char, class )
Let M be a matrix of a representation with character char which is a
character of the table tbl, for an element in the conjugacy class
class. Eigenvalues( tbl, char, class )
returns a list of
length n = tbl.orders[ class ]
where at position i
the
multiplicity of E(n)^i = e^{frac{2pi i}{n}}
as eigenvalue of M
is stored.
gap> t:= CharTable( "A5" );; gap> chi:= t.irreducibles[2]; [ 3, -1, 0, -E(5)-E(5)^4, -E(5)^2-E(5)^3 ] gap> List( [ 1 .. 5 ], i -> Eigenvalues( t, chi, i ) ); [ [ 3 ], [ 2, 1 ], [ 1, 1, 1 ], [ 0, 1, 1, 0, 1 ], [ 1, 0, 0, 1, 1 ] ]
List( [1..n], i - E(n)^i) * Eigenvalues(tbl,char,class) )
is equal to char[ class ]
.
GAP 3.4.4