Lie Groups Beyond an Introduction
《Lie Groups Beyond an Introduction》 · 第 187 页 · Chapter II，Section 9「Serre Relations」，Proposition 2.94
If we set $R'_i = q R_i^{-1}$, then the $R'_i$ still satisfy the braid relations, i.e., we have still $R'_i R'_{i+1} R'_i = R'_{i+1} R'_i R'_{i+1}$ and $R'_i R'_j = R'_j R'_i$ for $|j - i| \ge 2$, and we have additionally $(R'_i)^2 = (q^2 - 1) R'_i + q^2$ for all $i$. This implies that the subalgebra of $\operatorname{End}_U(V^{\otimes n})$ generated by the $R'_i$ is a homomorphic image of a Hecke algebra of type $A_{n-1}$.