On the combinatorics and geometry of (sub-) groups generated by reflections

• Applicant: Privatdozentin Dr. Barbara Baumeister
• Subject Area: Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 539960112

The project proposal concerns the dual approach to Coxeter and Artin groups within Garside theory. We combine different methods such as combinatorics, combinatorial geometry, group theory, and computer algebra to extend the dual approach fo general Coxeter groups and the related Artin groups. Our first main objective is to investigate for (affine) Coxeter groups W and for the elements w in W the correlation of Hurwitz transitivity of w, parabolic subgroups and the property of w to be a prefix of a (quasi)-Coxeter element, and to find a new, more satisfactory notion of a parabolic subgroup of W. Our second main objective is to understand the new class of groups G([1, 00w]) for the spherical (and affine) Coxeter groups and the proper quasi-Coxeter elements w in W, and possibly derive new results for the related mysterious Artin groups.

• DFG Programme: Priority Programmes
• Subproject of: SPP 2458: Combinatorial Synergies