Immanant of a matrix

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.

Immanant of a matrix

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.