Reflection length in affine Coxeter groups
- Noam von Rotberg (Otto-von-Guericke-Universität Magdeburg)
Abstract
In any Coxeter group the conjugate of elements in its Coxeter generating set are called reflections. The length of an element with respect to this expanded generating set is its reflection length.
This talk is about an explicit formula conjectured by Petra Schwer to compute reflection length in affine Coxeter groups. The authors bachelor thesis provides proofs for the conjectured formula in affine Coxeter groups of rank one and two and for one inequality in arbitrary rank. The general setting is unsolved so far.
In this talk, we consider example groups of rank one and two and develop the necessary notions as well as the statement of the conjecture alongside these examples. We see how the conjectured formula captures some of the groups’ structure and how it simplifies computation of reflection length.
