Level-two congruence subgroup conjecture for non-spherical small Coxeter groups
Level-two congruence subgroup conjecture for non-spherical small Coxeter groups
Let be a non-spherical small Coxeter graph, with associated Artin group , Coxeter group , and level-two congruence subgroup . Write for the level-two congruence subgroup of . Level-two congruence subgroup conjecture.
The preceding argument establishes the inclusion of the right-hand kernel in ; the conjecture asserts equality for every non-spherical small Coxeter graph. The parser provides no evidence of a resolution, so the conjecture remains open.
Sources & referencesView supporting material
Primary source
Pravin Kumar, “Congruence subgroups of small Artin and Coxeter groups”, arXiv:2510.23002 (2025).
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