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

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

2005-03-08

arxiv.org/abs/math/0503146v2

C. R. Acad. Bulg. Sci. 59 (2006), No. 5, 477-484

Mathematics

Rings and Algebras

25 pages

Scientific paper

Over a field of characteristic 0, the algebra of invariants of several $n\times n$ matrices under simultaneous conjugation by $GL_n$ is generated by traces of products of generic matrices. In this paper we have found, in terms of representation theory of $GL_2$, 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.

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