Given a symmetric function f, homogeneous of degree N, the method computes the corresponding virtual character of the symmetric group S_N.
The character of the standard representation of S_5 is
i1 : R = symmetricRing(QQ,5); |
i2 : classFunction(jacobiTrudi({4,1},R)) o2 = ClassFunction{{1, 1, 1, 1, 1} => 4} {2, 1, 1, 1} => 2 {3, 1, 1} => 1 {3, 2} => -1 {5} => -1 o2 : ClassFunction |
The character of the second exterior power of the standard representation of S_5 is
i3 : R = symmetricRing(QQ,5); |
i4 : classFunction(jacobiTrudi({3,1,1},R)) o4 = ClassFunction{{1, 1, 1, 1, 1} => 6} {2, 2, 1} => -2 {5} => 1 o4 : ClassFunction |
The object classFunction is a method function.