immanent
Let denote the symmetric group on elements.Let be a complex character
.For any matrix define the immanent of as
Special cases of immanents are determinants and permanents — in the case where is the constant character ( for all ), is the permanent of . In the case where is the sign of the permutation (which is the character of the permutation group
associated to the (non-trivial) one-dimensional representation), is the determinant of .