Software and computing
Software
The implementation of algorithms in the computer software CHEVIE and GAP4 are fundamental in the achievement of my joint results. Together with Dr. Tung Le, I am in the process of developing the GAP4 package iU.
The main features of the package are manipulating with elements of a unipotent subgroup U of finite groups of Lie type, and obtaining the relevant information for the generic parametrization of the irreducible characters of U and their character values.
The development of iU and its documentation are a work in progress. This is based on the list of functions and implemented algorithms which can be found here.
...and computing!
Luckily, or rather not, long explicit computations are as much needed for obtaining results as they are recommended not to appear in a published version of relevant work.
Perhaps the main use of this domain is to keep in a safe place such computations. These will be needed by the next person taking over the projects we have been working on.
I have decided to collect here all the computations that could not find space in the final version of my joint articles. The content of these files has in no way been peer reviewed.
The implementation of algorithms in the computer software CHEVIE and GAP4 are fundamental in the achievement of my joint results. Together with Dr. Tung Le, I am in the process of developing the GAP4 package iU.
The main features of the package are manipulating with elements of a unipotent subgroup U of finite groups of Lie type, and obtaining the relevant information for the generic parametrization of the irreducible characters of U and their character values.
The development of iU and its documentation are a work in progress. This is based on the list of functions and implemented algorithms which can be found here.
...and computing!
Luckily, or rather not, long explicit computations are as much needed for obtaining results as they are recommended not to appear in a published version of relevant work.
Perhaps the main use of this domain is to keep in a safe place such computations. These will be needed by the next person taking over the projects we have been working on.
I have decided to collect here all the computations that could not find space in the final version of my joint articles. The content of these files has in no way been peer reviewed.
- The structure constants of endomorphism algebras of Gelfand-Graev representations in rank 2. The main feature is the output an algorithm for left U-cosets representatives in a finite reductive group G, U being a Sylow p-subgroup. The output also serves as a setup for equations to determine the structure constants of such algebras. Click here for the algorithm code deposited in GitHub and a detailed version of the computations in types A_2 and B_2. This is joint work with I. Simion.
- The analysis of the nonabelian cores in types D_6 and E_6. Click here for the GAP4 code files to access functions and records for the examination of nonabelian cores of UD_6(q) and UE_6(q) and for the expanded computations related to the parametrisation of the irreducible characters arising from such nonabelian cores. This has been obtained jointly with Dr. Tung Le and Dr. Kay Magaard.
- The decomposition numbers of SO_8(2^f). The two main kind of computation records which are crucial for the result are the character values in the unipotent radical of SO_8(2^f) and the decomposition of Deligne-Lusztig characters into certain \ell-projectives. Click here for a detailed version of such computations.