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...

The relation between facets of Rees cones of clutters and irreducible b-vertex covers is examined. Let G be a simple graph and let Ic(G) be its ideal of vertex covers. We give a graph theoretical description of the irreducible bvertex covers of G, i.e., we describe the minimal generators of the symbolic Rees algebra of Ic(G). As an application we recover an explicit description of the edge cone...

The main combinatorial result in this article is a classification of bar partitions of n which are of maximal p-bar weight for all odd primes p ≤ n. As a consequence, we show that apart from very few exceptions any irreducible spin character of the double covers of the symmetric and alternating groups vanishes on some element of odd prime order.

Let H P denote the Hilbert scheme of smooth connected curves in P. We consider maximal irreducible closed subsets W ⊂ H P whose general member C is contained in a smooth cubic surface and investigate the conditions for W to be a component of (H P )red. We especially study the case where the dimension of the tangent space of H P at [C] is greater than dimW (≥ 4 deg(C)) by one. We compute obstruc...

In this paper we complete the classification of the primitive permutation groups of degree less than 1000 by determining the irreducible subgroups of GL(n, p) for p prime and pn < 1000. We also enumerate the maximal subgroups of GL(8, 2), GL(4, 5) and GL(6, 3). © 2003 Elsevier Science Ltd. All rights reserved. MSC: 20B10; 20B15; 20H30

For every hyperbolic group and more general hyperbolic graphs, we construct an equivariant ideal bicombing: this is a homological analogue of the geodesic flow on negatively curved manifolds. We then construct a cohomological invariant which implies that several Measure Equivalence and Orbit Equivalence rigidity results established in [MSb] hold for all non-elementary hyperbolic groups and thei...

For every hyperbolic group and more general hyperbolic graphs, we construct an equivariant ideal bicombing: this is a homological analogue of the geodesic flow on negatively curved manifolds. We then construct a cohomological invariant which implies that several Measure Equivalence and Orbit Equivalence rigidity results established in [MSb] hold for all non-elementary hyperbolic groups and thei...