Mathieu's approach to the Jacobian Conjecture

Abstract

In this paper, we give an expository presentation of the paper of Olivier Mathieu. The paper of Mathieu proves that a Lie group-theoretic conjecture implies the Jacobian Conjecture. To give Mathieu's proof, we first review the required literature on representation theory in an expository way. We continue to prove some results on the irreducible subrepresentations of the tensor algebra of the standard representation of $SL(N,\mathbb{C})$. The last part of the paper is dedicated to Mathieu's proof.