The ring of quasi-invariants of the dihedral group (Q1584116)

The authors prove the following assertion. The ring of quasi-invariants of the dihedral group \(D_N\) is generated by the polynomials \(z\overline z\), \(lz^k+k(z\overline z)^{\frac{k-l}{2}}\overline z^l\), \(l\overline z^k+k(z\overline z)^{\frac{k-l}{2}}z^l\), where \(k+l=2N\), \(k\geq l\geq 1\), \(N\geq 2\).