The "kgpgraph" command produces a 'dot' file containing the
closure relations for the orbits of K on the partial flag
variety G/P. This file can be processed by the free graph
visualization program 'dot' available from
http://www.graphviz.org.
Use the commands 'kgp' and 'kgporder' to view this infomation
in plain text form.
The software will prompt the user for a realform if it has not
already been chosen. The user is then prompted to enter a subset
of the simple roots corresponding to the desired parabolic. The
input should be a list of integers in [1,rank], separated by any
whitespace or non-numeric character(s). Numbers outside this
range are ignored.
After the parabolic subgroup is chosen, the user is prompted to
enter an output file. Generally this should be the name of an
ASCII text file ending in '.dot'. If no file name is entered, the
command is aborted.
For example:
empty: type
Lie type: B2 sc s
main: realform
(weak) real forms are:
0: so(5)
1: so(4,1)
2: so(3,2)
enter your choice: 2
real: kgpgraph
enter simple roots (1-2): 1
kgp size for roots {1}: 4
Name an output file (return for stdout, ? to abandon): spin32_1.dot
real:
Here the quasi-split form of type B2 is chosen, with P corresponding
to the root subset consisting of the unique long simple root, and an
output file name of 'spin32_1.dot'. To convert this to a visual graph
(assuming 'dot' is intsalled on the local system and in the users path)
exit Fokko and type:
dot -Tps -ospin32_1.dot spin32_1.ps
This will create a '.ps' file named 'spin32_1.ps' containing a picture
of the closure poset. Attempting to generate pictures from extremely
large posets is not recommended.
In the graph there is one vertex for each element of K\G/P labelled
according to the output of the 'kgp' command. A gray edge appears
connecting vi to vj (i > j) if orbit j is an immediate predecessor
to orbit i in the closure poset.