INTRO: If the cells in the W-graph of a block for some real Lie group are contracted down to points, then the result is an acyclic graph. The transitive closure of this graph is a poset, and this poset is closely related to the inclusions of closures of nilpotent orbits. The programs provided here are for producing snazzy graphic illustrations of these posets. I've used these programs on linux; they might work on Mac OS X; probably not on Windows. Update: David V informs me that it does work on Mac OS X, but you should expect to use awk (not gawk), and the OS X version of GraphViz seems to provide GUI tools, but no command line tools. REQUIRES: * gawk or some other awk-compatible scripting language, * a command line version of maple, * the 'posets' maple package (included). Also, it will be mostly useless unless you also have * the atlas software -- otherwise, you won't be able to produce the input files for these scripts, * the GraphViz package -- otherwise, you won't be able to process the output files into various graphics formats. GETTING STARTED: Download all of the files in this directory into a convenient location, such as a subdirectory of your home directory. If you have wget, do wget -nH -np -r --cut-dirs=2 \ http://www.math.lsa.umich.edu/~jrs/data/squashblock/ This will download the files into a directory named 'squashblock'. Edit the 'squash' script, so that it has correct paths to your local installation of 'gawk' (or awk) and command-line maple. The command which gawk can help you find this path. Confirm that the execute bit is enabled for 'squash': chmod u+x squash USAGE: The main program is the shell script 'squash'. It takes one argument, the output file produced by an instance of 'wcells' in atlas. It sends to the standard output a description of the poset in the dot language (the markup language used by GraphViz). You can then use the 'dot' command from GraphViz to convert this description into various graphics formats. EXAMPLE: Use 'atlas' to save the output of a 'wcells' command to a file. In this example, we've run wcells on a block of size 9576 for a real form of E7, and saved it to the file '/tmp/E7_sc_s23'. Now produce the dotfile: ./squash /tmp/E7_sc_s23 > E7_32.dot Now generate layouts in 'png' and 'ps' formats: dot -Tpng -o E7_32.png E7_32.dot dot -Tps -o E7_32.ps E7_32.dot We've included these particular output files for reference purposes. TIPS: Included in the dot output produced by 'squash' is a size command that scales the figure to fit and be centered in a 6.5 inch by 10.0 inch box. (Suitable for US letter paper.) For displaying larger graphs on monitors, you may want to crank up the height of this box to 20 inches or more. There are *many* features in dot for endless tinkering. To get started, look for 'dotguide.pdf' in the GraphViz package. You can get E8 wcells output files from Birne Binegar: . Enjoy. John Stembridge 26 March 2008