Immanant
In mathematics, the immanant of a matrix was defined by Dudley E. Littlewood and Archibald Read Richardson as a generalisation of the concepts of determinant and permanent.
Let be a partition of and let be the corresponding irreducible representation-theoretic character of the symmetric group. The immanant of an matrix associated with the character is defined as the expression
The determinant is a special case of the immanant, where is the alternating character, of Sn, defined by the parity of a permutation.
The permanent is the case where is the trivial character, which is identically equal to 1.
For example, for matrices, there are three irreducible representations of, as shown in the character table:
As stated above, produces the permanent and produces the determinant, but produces the operation that maps as follows:
Littlewood and Richardson also studied its relation to Schur functions in the representation theory of the symmetric group.
