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

Vesselin Drensky; Liliya Sadikova

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

Rings and Algebras 2007-05-23 v2 Commutative Algebra

Authors: Vesselin Drensky , Liliya Sadikova

Abstract

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.

Keywords

invariants of matrices simultaneous conjugation gl_n traces of products gl_2 representation theory minimal generators combinatorial proof

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@article{arxiv.math/0503146,
  title  = {Generators of Invariants of Two $4 \times 4$ Matrices},
  author = {Vesselin Drensky and Liliya Sadikova},
  journal= {arXiv preprint arXiv:math/0503146},
  year   = {2007}
}

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25 pages

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

Abstract

Keywords

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