J. Matthew Douglass

On Reflection Subgroups of Finite Coxeter Groups

Let W be a finite Coxeter group. We classify the reflection subgroups of W up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup R of W the conjugacy class of its Coxeter elements to be injective, up to conjugacy.

Cohomology of Coxeter arrangements and Solomon's descent algebra

We refine a conjecture by Lehrer and Solomon on the structure of the Orlik-Solomon algebra of a finite Coxeter group

Homology of generalized Steinberg varieties and Weyl group invariants

W

Computations for Coxeter arrangements and Solomon's descent algebra: Groups of rank three and four

and relate it to the descent algebra of

Computations for Coxeter arrangements and Solomon's descent algebra III: Groups of rank seven and eight

W

INVARIANTS OF REFLECTION GROUPS, ARRANGEMENTS, AND NORMALITY OF DECOMPOSITION CLASSES IN LIE ALGEBRAS

. As a result, we claim that both the group algebra of

An inversion formula for relative kazhdan—lusztig polynomials

W

On the cohomology of an arrangement of type B1

, as well as the Orlik-Solomon algebra of

An inductive approach to Coxeter arrangements and Solomon's descent algebra

W

The Steinberg variety and representations of reductive groups

can be decomposed into a sum of induced one-dimensional representations of element centralizers, one for each conjugacy class of elements of