2
$\begingroup$

Coxeter group $I_2(n)$ is just a dihedral group $D_{2n}$. This group acts on the plane $\mathbb{R}^2$ and after complexification on $\mathbb{C}^2$, thus it acts on $\mathbb{C}[z_1, z_2]$. Ring of invariants $\mathbb{C}[z_1, z_2]^{D_{2n}}$ is again ring of polynomial on two independent invariants $p_1$ and $p_2$ i.e. $\mathbb{C}[z_1, z_2]^{D_{2n}}=\mathbb{C}[p_1, p_2]$. Could someone explain to me (or give a reference) how one can get an equation of the discriminant(=image of all irregular orbits) in the orbit space?

  • 1
    In general, Humphreys' *Reflection groups and Coxeter groups* is a good reference for anything pertaining to Coxeter groups2012-08-05

1 Answers 1