Dixmiera0a0a0a0Moeglin equivalence away from the zero ideal

Establish the Dixmiera0a0a0a0Moeglin equivalence for every nonzero prime ideal of the universal enveloping algebra U(W_{a0-1}), namely, prove that local closedness, primitivity, and rationality are equivalent for such prime ideals.

Background

The paper proves that each orbit-homomorphism image B_n satisfies the Dixmiera0a0a0a0Moeglin equivalence. In contrast, the zero ideal of U(W_{a0-1}) is known to be rational but not locally closed, so the full enveloping algebra does not satisfy the equivalence at that ideal.

The conjecture isolates the remaining expected valid range: all nonzero prime ideals of U(W_{a0-1}).