Unitriangularity of decomposition matrices for groups of Lie type

Establish unitriangularity of decomposition matrices for all groups of Lie type, thereby extending the unitriangularity results currently available only in restricted cases.

Background

The paper explains that earlier proofs of equivariance and extendibility often relied on unitriangular decomposition matrices. Because unitriangularity is unavailable in general, the authors instead use unimodularity of decomposition matrices and permutation-group arguments. A general proof of unitriangularity for groups of Lie type would therefore provide a broader structural tool for studying Brauer characters and related inductive conditions.

References

Unfortunately, unitriangularity has not been established for all groups of Lie type; in general, unitriangularity remains an open problem.

— The Brauer $A(\infty)$ condition and Navarro's conjecture on Brauer characters under coprime actions  (2609.26441 - Feng et al., 22 Sep 2026) in Section 1, Introduction