Characterization of weighted restrictions admitting effective chamber-orbit relations

Determine which weighted restrictions admit a chamber-orbit relation strong enough to reduce all associated projective chamber periods to classical beta, Dixon, or Selberg integrals.

Background

The paper proves a Stokes relation showing that, under critical homogeneity and strict flat-integrability conditions, the positive projective chamber-period vector lies in the kernel of the associated Varchenko matrix. In the F4 and D5 cases, finite chamber-orbit decompositions make this relation sufficiently strong to transfer one classically evaluable period to the remaining periods. The paper leaves unresolved the broader classification of weighted restrictions for which such a chamber-orbit relation determines all periods from beta, Dixon, or Selberg integrals.