Proof of the BMR conjecture for 2-reflection groups

Proof of the BMR conjecture for 2-reflection groups (with G. Pfeiffer)

The method that we followed in our article The BMR freeness conjecture for the 2-reflection groups is based on algorithms that we implemented in GAP3. Before launching them, you will need to install GAP3 as well as the development version of the CHEVIE package. This one can be found on Jean Michel's webpage at the address http://webusers.imj-prg.fr/~jean.michel/chevie/index.html. At this address you will find the latest version available. However, there is no insurance that this latest version is still compatible with the one we used (in particular w.r.t. the basic datas stored there concerning the complex reflection groups). Therefore, you will find here the install version we used in order to execute these programs. The programs we used for the first version (on the arxiv) of our preprint can be found here . For version 2, we improved the programs by using sparse vectors. A reasonably streamlined version (still improving) can be found here. For the time being (august 2015), the special case of G34 needs a bunch of separate programs, which are not that easy to undersand, in order to get the result in 3 weeks, as promised by the preprint. Until we improve the general program, one thus needs to use the programs for this special case. The corresponding log file can be found here. It contains the ordering used by the program to fill in the table, and therefore can be used in order to quickly prove the conjecture : one just needs to plug in artificially the ordered list of entries to be computed -- thus avoiding the long trial-and-error process, which is by far the most time-consuming part of our program.

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