In Proposition 6.3.3 in Casselman's notes on representation theory of $p$-adic groups, I believe there is an error in the statement of the Proposition.
Let $G$ be the points of a connected, reductive group over a $p$-adic field $k$, $A_0$ a maximal split torus with $P_0 = M_0N_0$ a minimal Levi and $P_{\theta} = M_{\theta}N_{\theta}$ a standard parabolic subgroup for $\theta \subset \Delta$.
If $\Sigma$ is the set of reduced roots of $A_0$ in $G$, then the modulus character $\delta_{P_{\theta}}$ for $P_{\theta}$ is given by the sum of the roots of $A_0$ in $N_{\theta}$, written multiplicatively as
$$\prod\limits_{\alpha \in \Sigma^+ \backslash \Sigma_{\theta}^+} \alpha^{m_{\alpha}}$$
where $m_{\alpha}$ is an associated multiplicity. For $\Omega \subset \Delta$, one considers an element $w$ in the Weyl group $W$ such that $w$ is the element of smallest length $W_{\theta}wW_{\Omega}$, and a representative $x \in N(A_0)$ of $w$. One considers the modulus character $\gamma$ of $N_{\Omega}/(N_{\Omega} \cap x^{-1}P_{\theta}x)$, and the character $(w^{-1}\delta_P^{\frac{1}{2}})\gamma$.
The first statement "The character $(w^{-1} \delta_{\theta}^{\frac{1}{2}}) \gamma$ is thus the square root of the norm of the rational character equal to..." looks good. But then "This in turn is equal to..." doesn't look right. In fact, none of these three products are equal to another, as far as I can tell.
For example, let me try to show directly the equality of the first and the third terms:
$$\prod\limits_{\alpha \in \Sigma^+ \setminus \Sigma_{\theta}^+} w^{-1}\alpha^{m(\alpha)} \prod\limits_{\substack{\alpha \in \Sigma^+ \setminus \Sigma_{\Omega}^+ \\ w\alpha \in \Sigma^- \setminus \Sigma_{\theta}^-}} \alpha^{2m(\alpha)} = \prod\limits_{\substack{\alpha \in \Sigma^+ \setminus \Sigma_{\Omega}^+\\ w\alpha \in \Sigma^- - \Sigma_{\theta}^-}} \alpha^{m(\alpha)} \prod\limits_{\substack{\alpha \not\in \Sigma^+ \setminus \Sigma_{\Omega}^+ \\ w\alpha \in \Sigma^- \setminus \Sigma_{\theta}^-}} \alpha^{-m(\alpha)}$$
This is equivalent to
$$\prod\limits_{\alpha \in \Sigma^+ \setminus \Sigma_{\theta}^+} w^{-1}\alpha^{m(\alpha)} \prod\limits_{\substack{\alpha \in \Sigma^+ \setminus \Sigma_{\Omega}^+ \\ w\alpha \in \Sigma^- \setminus \Sigma_{\theta}^-}} \alpha^{m(\alpha)} = \prod\limits_{\substack{\alpha \not\in \Sigma^+ \setminus \Sigma_{\Omega}^+ \\ w\alpha \in \Sigma^- \setminus \Sigma_{\theta}^-}} \alpha^{-m(\alpha)}$$
which is equivalent to
$$\prod\limits_{\alpha \in \Sigma^+ \setminus \Sigma_{\theta}^+} w^{-1}\alpha^{m(\alpha)} = \prod\limits_{ w\alpha \in \Sigma^- \setminus \Sigma_{\theta}^-} \alpha^{-m(\alpha)}$$
As far as I can tell, this last equality is not true unless $w = w_l w_l^{\theta}$, which is to say that $w$ is the canonical coset representative in $W_{\theta} \backslash W$ of largest length. In general, $w^{-1}(\theta) > 0$, but some of the roots in $w^{-1}. \Sigma^+ - \Sigma_{\theta}$ may remain positive.
Oh wait nevermind it is true..the last product I wrote, is equal to $$\prod\limits_{w \alpha \in \Sigma^+ \setminus \Sigma^+_{\theta}} \alpha^{m(\alpha)}$$ which is definitely equal to $$\prod\limits_{ \alpha \in \Sigma^+ \setminus \Sigma^+_{\theta}} w^{-1} \alpha^{m(\alpha)}$$
So this proposition in Casselman's notes is correct after all.