Proof of `Formal coordinates on the annihilator of a Lie subalgebra` (5th statement)
What this proof establishes
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
PBW-dual coordinates give a diagonal moment matrix: a shuffle monomial pairs only with its matching complementary PBW monomial, with factorial value.