Immanant of a matrix
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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
This generalizes the notions of determinant and permanent, the determinant being the case where χλ is the alternating character sgn, and the permanent being the case where χλ 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.
[edit] References
- D.E. Littlewood and A.R. Richardson, Group characters and algebras, Philosophical Transactions of the Royal Society (1934)
