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2. Classification of maximal reflective arithmetic lattices

Restricting to dimensions n \geq 2, there are only finitely many maximal reflective arithmetic hyperbolic lattices. One driving goal is to find an exhaustive list of such lattices that are
  1. uniform and defined over \mathbb{Q}.
  2. non-uniform and defined over \mathbb{Q}.
  3. uniform and defined over a number field k/\mathbb{Q}.
Of course, in practice, these three types of lattices may require different approaches and techniques.
    1. Problem 2.1.

      Scharlau has recently classified all non-uniform lattices in dimensions n=3 and n=4 (possibly also n = 5?). It is known that such lattices do not exist when n=20 or when n \geq 22. When n=21, there is only one reflective arithmetic lattice. Can we classify all non-uniform lattices the remaining n-values?
        • Problem 2.2.

          Can we classify all non-uniform maximal reflective arithmetic lattices when n=6? How about just those that are congruence?
            • Problem 2.3.

              Can we classify non-uniform maximal reflective arithmetic lattices in dimensions n \geq 10? How about just those that are congruence?
                • Problem 2.4.

                  For n=19, there is only one known example of a non-uniform reflective arithmetic lattice. Is it unique, which is the case for the lone example in dimension 21?
                    • Problem 2.5.

                      Create a central repository (similar to the LMFDB) for all known data relating to Coxeter polytopes in low-dimension.

                          Cite this as: AimPL: Arithmetic reflection groups and crystallographic packings, available at http://aimpl.org/reflectiongpv.