Twisted non-symmetric triad

Construct the triad for twisted non-symmetric Cherednik eigenfunctions, at least for the twisted Cherednik integrable systems with t=q^{-m}, m\in\mathbb{Z}_{\ge 0}.

Background

The paper identifies twisted Cherednik integrable systems as a natural extension of the non-twisted systems studied. Twisted Baker–Akhiezer functions and their associated eigenfunctions are known, but the corresponding triad construction for non-symmetric eigenfunctions is not provided.

The authors also note that even the notion of a twisted triad in the symmetric case has not been developed, making the non-symmetric extension a broader unresolved problem.

References

However, generalization of the triad to the twisted non-symmetric eigenfunctions remains for the future studies.

— Non-symmetric triads and Baker-Akhiezer functions  (2609.01517 - Mironov et al., 1 Sep 2026) in Section 6, “Conclusion”

There are some problems there with constructing explicit formulas for universal solutions, as was pointed out in cite{BMP}, and it is unclear to what extend explicit formulas for the triad could be obtained in this case.

— Non-symmetric triads and Baker-Akhiezer functions  (2609.01517 - Mironov et al., 1 Sep 2026) in Section 6, “Conclusion”