### Spherical Unitary Explorer for Classical Groups

This is the beta version the explorer for all classical groups. Please send
bugs to jda@math.umd.edu.

This is a program for learning about the spherical unitary representations of
a real or p-adic classical group G. A spherical representation of G is given by a
parameter lambda, which is an n-tuple of complex numbers; after a basic reduction we assume
lambda is real. It implements an algorithm in a paper by Dan Barbasch.

Choose a type (A-D), enter a parameter lambda and click Test. A popup window will tell you whether the corresponding
irreducible spherical representation of G is unitary, together with some supplementary
data about the representation. Lambda is entered a as a string of real numbers, separated by commas or spaces (it will be made dominant).
For example: **.75 1 1/2 0** or **2,1/2,-.5,-2**

For more information see the help page

You might also be interested in the command line version of this program.

There is also a page with information on Root Systems and Coordinates and a pdf file on the mathematics behind this program.

Return to the Atlas home page

**Test a single point:**