## Immanant

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

where the summation is over the permutations of the Symmetric Group and

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.