Let $P_0$ be a minimal $\mathbb{Q}$ parabolic subgroup of $G$ semisimple linear algebraic group over $\mathbb{Q}$. $P_0 = M_0 N_0$ where $M_0$ is a Levi subgroup of $P_0$. And $E^G_{P_0}$ is the Eisenstein series $$ E^G_{P_0}(\lambda, g) = \sum_{\gamma \in P(\mathbb{Q}) \backslash G(\mathbb{Q}) } exp(<\lambda + \rho_{P_0}, H_{P_0} (\gamma g) >). $$ Let $$ c(w, \lambda) = \int_{ (w' N_0(\mathbb{A})(w')^{-1} \cap N_0 (\mathbb{A})) \backslash N_0(\mathbb{A}) } exp(<H_{P_0} ((w')^{-1}n) , \lambda+ \rho_{P_0} >) dn. $$ I am wondering what is meant by "the singular hyperplanes of $c(w, \cdot)$"?

This is in Lemma 7 (p 429) of the paper https://link.springer.com/content/pdf/10.1007/BF01393904.pdf which states: The singular hyperplanes of $c(w, \cdot)$ containing $\rho_{P_0}$ are precisely the hyperplanes $$ <\check{\alpha}, \lambda - \rho_{P_0}> = 0 $$ where $\alpha$ is a simple positive root such that $w \alpha$ is a negative root.

I would like to understand the statement of this lemma. I have been going through definitions but I have not been able to do this yet. I would greatly appreciate any explanation on this. Thank you very much.