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 jda@math.umd.edu.

There is also a downloadable command line version of the software.