This section of the Atlas will contain information on spherical unitary representations.
I'm working on putting in some data for various groups. At the moment see C2, C3 and C4.
Dan Barbasch has computed the spherical unitary dual of any split real or p-adic classical group (Unitary Spherical Dual of Split Classical Groups). 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.
On-line Spherical Explorer for Sp(2n):
This is a web-based tool for exploring the spherical unitary dual of Sp(2n). You may enter individual points, or files. There are examples provided.
This is a beta version. Comments are welcome.
Command Line Spherical Explorer for Sp(2n):
A perl program to test spherical representations of Sp(2n) for unitarity. Implements Barbasch's algorithm. It will test individual points from the command line, or a set of points from a file.
To use this program download it to your computer (using right mouse click). Make it executable (chmod u+x sph.pl). Give the command
sph.pl.
For help do
sph.pl -h.
There are a few more tips at the top of the file itself.
You can try the program by running it on a file "all" or "allPsd" from one of the subdirectories. These give a list of representative points from every facet, and only those which are unitary, respectively. Currently some data are available for C2, C3 and C4.
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