Abstract
In this paper we study the variety M nil of nilpotent elements of a reductive monoid M. In general this variety has a completely different structure than the variety G uni of unipotent elements of the unit group G of M. When M has a unique non-trivial minimal or maximal G×G-orbit, we find a precise description of the irreducible components of M nil via the combinatorics of the Renner monoid of M and the Weyl group of G. In particular for a semisimple monoid M, we find necessary and sufficient conditions for the variety M nil to be irreducible.
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Putcha, M.S. Nilpotent variety of a reductive monoid. J Algebr Comb 27, 275–292 (2008). https://doi.org/10.1007/s10801-007-0087-y
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DOI: https://doi.org/10.1007/s10801-007-0087-y