50.8 Eigenvalues

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 ].

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