Denote by $P^{I,y}_{x,w}$ be the parabolic Kazhdan-Lusztig polynomial of ${}^IW$ of type $y$. I have heard that the polynomials $P^{I,q}_{x,w}$ give the transition matrix between a canonical basis and standard basis $\{T_w\}$ of $M^I$, where $M^I \cong \text{Ind}_{W_I}^W (\text{triv})$. Note that $T_s$ act as multiplication by $q$ on the trivial module. See [here][1]. **My questions:** 1. Is the above statement correct? 2. What is about the polynomials $P^{I,-1}_{x,w}$? [1]: https://mathoverflow.net/questions/325436/about-%20parabolic-kazhdan-lusztig-polynomials