invariant theory

In mathematics, invariant theory refers to the study of invariant algebraic forms (equivalently, symmetric tensors) for the action of linear transformations. This was a major field of study in the latter part of the nineteenth century, when it appeared that progress in this particular field (out of any number of possible mathematical formulations of invariance with respect to symmetry) was the key algorithmic discipline. Despite some heroic efforts that promise was not fulfilled but many spin-off advances are connected to this research. Current theories relating to the symmetric group and symmetric functions, commutative algebra, moduli spaces and the representations of Lie groups are rooted in this area.
See more at Wikipedia.org...