I am reading Casselman and Shalika's paper, the unramified principla series of p-adic groups II.
I have a problem on the special unitary group $SU(3)$ over local p-adic field.
Let $F$ be a local field with $\mathfrak o_F$ and $\mathfrak p_F$ the integral rings and the maximal prime ideal, respectively. Let $E/F$ be an unramified quadratic extension and $$G=SU_3(F)=\{g\in SL_3(E),\quad g=J({}^T\overline g)^{-1}J \}$$ where $J=\begin{pmatrix}&&1\\&1\\1\end{pmatrix}$.
The unipotent radical of the standard minimal parabolic subgroup of $G$ is $$ N=\left\{\begin{pmatrix}1&x&y\\&1&-\overline x\\&&1\end{pmatrix},x,y\in E, Norm(x)=-Tr(y)\right\}. $$ Let $$ N_0=\left\{\begin{pmatrix}1&x&y\\&1&-\overline x\\&&1\end{pmatrix}\in N,x,y\in\mathfrak o_E\right\}, $$ $$ N_1=\left\{\begin{pmatrix}1&x&y\\&1&-\overline x\\&&1\end{pmatrix}\in N,x\in\mathfrak o_E,y\in\mathfrak p_E\right\}. $$ Obviously $N_0\supset N_1$. If we normalize the Haar measure on $N$ such that $Vol(N_0)=1$, how to obtain $Vol(N_1)$?
Thanks!