Spin Representations with Negative Indices

Habre, Samer S.; Al-Tahan, Madline; Abdulrahim, Mohammad N.

Spin Representations with Negative Indices

Habre, Samer S.; Al-Tahan, Madline; Abdulrahim, Mohammad N.

URI: http://hdl.handle.net/10725/2138

URL: http://journals.math.tku.edu.tw/index.php/TKJM/article/view/1457

DOI: http://dx.doi.org/10.5556/j.tkjm.45.2014.1457

Date: 2017-04-26

Abstract:

We consider the spin representation of Artin’s braid group, which has a negative index of one and was originally given by D. D. Long and explicitly computed by J.P.Tian. In our work, we find sufficient conditions under which the complex specialization of that representation, namely α : Bn → GLn 2 (C), is unitary relative to a nonsingular hermitian matrix