Centralizer of an idempotent in a reductive monoid

Let

FINE BRUHAT INTERSECTIONS FOR REDUCTIVE MONOIDS

This paper concerns Bruhat intersections for a reductive monoid M. A comparison is made to the known results for Bruhat intersections for a reductive group G.

PARABOLIC MONOIDS I: STRUCTURE

We determine the closure of a parabolic subgroup of a reductive group in a reductive monoid. This allows us to define parabolic submonoids of a finite monoid of Lie type. These are analogues of the monoid of block upper triangular matrices. We determine the structure of [Formula: see text]-class of a finite parabolic monoid and show that such a monoid is generated by its unit group and diagonal idempotents.

An Explicit Cell Decomposition of the Wonderful Compactification of a Semisimple Algebraic Group

We determine an explicit cell decomposition of the wonderful compactification of a semisimple algebraic group. To do this we first identify the B × B-orbits using the generalized Bruhat decomposition of a reductive monoid. From there we show how each cell is made up from B × B orbits.

Conjugacy Classes and Nilpotent Variety of a Reductive Monoid

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 Mnil 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.