A NEW COMPUTER CONSTRUCTION OF THE IRREDUCIBLE 112-DIMENSIONAL 2-MODULAR REPRESENTATION OF JANKO'S GROUP J₄

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ACKNOWLEDGMENTS

The authors of this paper have been supported by the DFG research project “Algorithmic Number Theory and Algebra”.

A substantial part of the high performance computations proving Theorem 1.4 were conducted using the resources of the Cornell Theory Center, which receives major funding from the National Science Foundation and New York State with additional support from the Research Resources at the National Institutes of Health, IBM Cooperation and members of the Corporate Research Institute. The total computing time on all the involved nodes was 28137 CPU-h. We owe special thanks to Professor J. Guckenheimer and Dr. A. Hoisie for their support.

The authors also would like to thank the Computer Center of Karlsruhe University for providing 38785 CPU-h on their supercomputer IBM RS/6000 SP with 256 knots. This help was necessary to complete the above mentioned computations. We are very grateful to Professor W. Schönauer for his assistance.

We also have to thank Dipl.-Math. M. Kratzer for his great computational assistance with several calculations described in Remark 4.7.