|Spherical Unitary Representations|
Dan Barbasch has computed the spherical unitary dual of any split real or p-adic classical group: The unitary spherical spectrum for split classical groups J. Inst. Math. Jussieu 9 (2010), no. 2, 265-356. Here is an expository version of the first few sections of this paper, with an emphasis on the algorithm which is implemented in the Spherical Explorer.
Here is the On-line Spherical Explorer
for studying the spherical unitary dual of classical groups. You may enter individual points, or list of points from files. There are examples provided.
This is a beta version. Comments are welcome: send email to firstname.lastname@example.org.
There is also a downloadable command line version of the software.