BIG JORDAN BLOCKS IN THE IMAGES OF UNIPOTENT ELEMENTS OF NONPRIME ORDER IN IRREDUCIBLE REPRESENTATIONS OF SPECIAL LINEAR AND SYMPLECTIC GROUPS
Abstract
For special linear and symplectic groups of not too small ranks with respect to p over a field of an odd characteristic p and p-restricted irreducible representations of а general form, lower estimates for the number of Jordan blocks of size >ps in the images of unipotent elements of order ps+1 > p in such representations are obtained. These estimates depend upon the group rank, the characteristic and the value of the highest weight of the representation on the maximal root of the group. These results are aimed at searching “rare” classes of unipotent elements that can be useful for solving recognition problems for representations and linear groups.
Supporting agencies: Their research is supported by the Belarussian Republican Foundation for Fundamental Research (Project Ф14Р-109).
About the Author
Irina D. Suprunenko
Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk
Belarus
Belarus
D. Sc. (Physics and Mathematics), Chief researcher
11, Surganov Str., 220072
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