Generators of Invariants of Two $4\times 4$ Matrices

Abstract

Over a field of characteristic 0, the algebra of invariants of several $n\times n$ matrices under simultaneous conjugation by $G{L}_n$ is generated by traces of products of generic matrices. In this paper we have found, in terms of representation theory of $G{L}_2$, a minimal set of generators of the algebra of invariants of two $4\times 4$ matrices. The proof is purely combinatorial and involves computer calculations with standard functions of Maple.

25 pages

References in corpus (1)

• Defining relations of invariants of two 3 \times 3 matrices