For an matrix, let denote any permutation , , ..., of the set of numbers 1, 2, ..., ,
and let
be the character of the symmetric group corresponding to the partition . Then the
immanant
is defined as
See also Determinant, Permanent
References
Littlewood, D. E. and Richardson, A. R. ``Group Characters and Algebra.'' Philos. Trans. Roy. Soc. London A 233, 99-141, 1934.
Littlewood, D. E. and Richardson, A. R. ``Immanants of Some Special Matrices.'' Quart. J. Math. (Oxford) 5, 269-282, 1934.
Wybourne, B. G. ``Immanants of Matrices.'' §2.19 in Symmetry Principles and Atomic Spectroscopy. New York: Wiley, pp. 12-13, 1970.