- Immanant redirects here; it should not be confused with the philosophical immanent.
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 n and let χλ be the corresponding irreducible representation-theoretic character of the symmetric group Sn. The immanant of an 
matrix A = (aij) associated with the character χλ is defined as the expression
The determinant is a special case of the immanant, where χλ is the alternating character sgn, of Sn, defined by the parity of a permutation.
The permanent is the case where χλ is the trivial character, which is identically equal to 1.
Littlewood and Richardson also studied its relation to Schur functions in the representation theory of the symmetric group.
References
- D.E. Littlewood; A.R. Richardson (1934). "Group characters and algebras". Philosophical Transactions of the Royal Society, Ser. A 233: 99–124. doi:.
External links
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