Rational Invariants of Even Degree Polynomials Under the Orthogonal Group

Abstract

In this article, we construct a generating set of rational invariants for the action of the orthogonal group O(n) on the space  R[x_1,..., x_n]_{2d} of real homogeneous polynomials of even degree 2d. This generalizes a paper which addressed the case n=3.     The main difficult with the generalization lies in a surprising connection to the graph isomorphism problem, a classical problem of computer science.

Keywords: Invariants, orthogonal group