Rational invariants of even degree polynomials under the orthogonal group

2025/01/29 by Breloer, Henri
#05C60 #13A50 (Primary) #68W30 (Secondary) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.17504

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[x₁,…,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.

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