Conjugacy classes and nilpotent variety of a reductive monoid

http://dx.doi.org/10.4153/CJM-1998-044-7
Canad. J. Math. 50(1998), 829-844

  Published:1998-08-01
 Printed: Aug 1998

We continue in this paper our study of conjugacy classes of a reductive monoid $M$. The main theorems establish a strong connection with the Bruhat-Renner decomposition of $M$. We use our results to decompose the variety $M_{\nil}$ of nilpotent elements of $M$ into irreducible components. We also identify a class of nilpotent elements that we call standard and prove that the number of conjugacy classes of standard nilpotent elements is always finite.