The Lie Groups $SO^+(3,1)$ and $SL(2,\mathbb{C})$ occupy a particular, unique place in physics. I am interested in the following problem: suppose I have a finite-dimensional representation (not necessarily irreducible!) of one of these groups. How can one classify of all the invariant polynomials under this representation?
2026-03-26 11:18:16.1774523896
What are the invariant polynomials of representations of the Lorentz group $SO^+(3,1)$ and $SL(2,\mathbb{C})$?
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The case $SL(2)$ is the well known problem of the classical invariant theory. You may find lists of invariants for example here