Compatibility of boundary cases between Weyl chambers

Determine whether boundary cases with coincident composition parameters fit continuously with the adjacent Weyl-chamber descriptions or instead form separate domain walls, and establish whether this behavior is a general feature or a peculiarity of the type A root system.

Background

The non-symmetric triad is organized into branches according to the ordering of the analytically continued composition parameters. When parameters coincide, the paper specifies a convention for assigning an order, but raises the possibility that such boundary cases might not belong naturally to either neighboring chamber.

The issue concerns whether genuine domain walls occur between Weyl chambers and whether the observed behavior extends beyond the type A setting.

References

A priori it could have happened that boundary cases not fit together with either \mu_1<\mu_2<\mu_3 chamber or \mu_1<\mu_3<\mu_2 chamber, instead forming domain walls. Wether this is a general phenomenon of a peculiarity of the A_N root system remains to be studied.

— Non-symmetric triads and Baker-Akhiezer functions  (2609.01517 - Mironov et al., 1 Sep 2026) in Section 5.4.2, subsection “Different branches”