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

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

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Test a single point:

Type:   lambda:       Coordinates:


File Examples:

Example Level of Detail
    Show unitary points only

All Unipotent Representations:
Type Rank Level of Detail

Upload a file containing a list of lambdas (see the help page for the format of the file):

Type File Level of Detail Coordinates
Show unitary points only