Speaker: Kyle Petersen, DePaul University
Title: Reflection length in Coxeter groups
Time: 2:30 PM, Monday, November 27, 2017
Place: Malott 206
Abstract: Every element in a Coxeter group can be expressed as a
product of reflections. The minimal number of reflections needed to
express the element $w$ is the *reflection length* of $w$. Reflection
length is additive with respect to direct products of groups, so it
suffices to consider reflection length in irreducible cases. Here we
have a trichotomy result about reflection length that ought to be
better known:
1) If $W$ is a spherical (finite) Coxeter group of rank $n$, reflection
length is bounded by $n$.
2) If $W$ is an affine Coxeter group of rank $n$, reflection length is
bounded by $2n$.
3) If $W$ is otherwise, reflection length is unbounded.
In the 1970s, Carter gave a geometric characterization of reflection
length in the spherical case; the length of an element $w$ is the
dimension of the "move-set" of $w$. I will describe a similar geometric
characterization of reflection length in the affine case, along with
some remarks about computing reflection length.
This is joint work with Joel Lewis, Jon McCammond, and Petra Schwer.
Back to main seminar page.