|
|
A typical element of the Siegel parabolic is given by $g$. I could get write the $d_{ij}$ in terms of $A$, but I think it would make it messier to look at.
|
The first coset rep is just the identity, so that just leaves $g$. The second set are of the following form with $z \in \mathbb{F}_{p}$.
|
Multiplied by a typical parabolic element:
|
The third set is given by reps of the following form with $y,z \in \mathbb{F}_p$.
|
Multiplied by a typical parabolic element:
|
Finally, the last type is given by the following form with $x,y,z \in \mathbb{F}_p$.
|
Multiplied by a typical parabolic element:
|
|