A reflection group has a reflection representation in the natural sense. But what is the reflection representation for a Coxeter group if its simple roots cannot be regarded as reflections in the Euclidean space?
In this paper, the author says that this is Definition 1.5 in
W. Soergel, Kazhdan-Lusztig-Polynome und unzerlegbare Bimoduln uber Polynomringen, J. Inst. Math. Jussieu 6 (2007), no. 3, 501–525.
But I don't have this paper and I can't read in German. Would anyone please give some help?