Nilpotent variety of a reductive monoid
نویسنده
چکیده
In this paper we study the variety Mnil of nilpotent elements of a reductive monoid M . In general this variety has a completely different structure than the variety Guni 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 Mnil 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 Mnil to be irreducible.
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