Affine twisted length function

Abstract

Let $W_a$ be an affine Weyl group. In 1987 Jian Yi Shi gave a characterization of the elements $w \in W_a$ in terms of $\Phi^+$-tuples $(k(w,\alpha))_{\alpha \in \Phi^+}$ called the Shi vectors. Using these coefficients, a formula is provided to compute the standard length of $W_a$. In this note we express the twisted affine length function of $W_a$ in terms of the Shi coefficients.