About: Weyl distance function

In combinatorial geometry, the Weyl distance function is a function that behaves in some ways like the distance function of a metric space, but instead of taking values in the positive real numbers, it takes values in a group of reflections, called the Weyl group (named for Hermann Weyl). This distance function is defined on the collection of chambers in a mathematical structure known as a building, and its value on a pair of chambers a minimal sequence of reflections (in the Weyl group) to go from one chamber to the other. An adjacent sequence of chambers in a building is known as a gallery, so the Weyl distance function is a way of encoding the information of a minimal gallery between two chambers. In particular, the number of reflections to go from one chamber to another coincides with