Example \(Sp(4,R)\)ΒΆ

Let us find all the \(K\backslash G/B\) elements of \(Sp(2,\mathbb R)\).

There are a couple of commands that will give you discrete series:

atlas> whattype discrete_series ?
Overloaded instances of 'discrete_series'
  (KGBElt,ratvec)->Param
  (RealForm,ratvec)->Param
atlas>
atlas>
atlas> whattype all_discrete_series_gamma ?
No overloads for 'all_discrete_series_gamma'
atlas>

NEED TO PUT HERE A DISCUSSION ON THE COMMAND all_discrete_series_gamma THAT WILL LIST THE FOUR D.S FOR SP4R.

This command lists all discrete series with the same parameters. The only things that is different is the element x.