A NOTE ON THE UNITARITY PROPERTY OF THE GASSNER INVARIANT

Abstract. We give a 3-page description of the Gassner invariant (or representation) of braids (or pure braids), along with a description and a proof of its unitarity property. The unitarity of the Gassner representation [Ga] of the pure braid group was discussed by many authors (e.g. [Lo, Ab, KLW]) and from several points of view, yet without exposing how utterly simple the formulas turn out to be1. When the present author needed quick and easy formulas, he couldn’t find them. This note is written in order to rectify this situation (but with no discussion of theory). I was heavily influenced by a similar discussion of the unitarity of the Burau representatio