8 citations · 19 across the 19 of their papers we have counts for
5 papers · 1 filter
Spherical subgroups in reductive algebraic groups
Friedrich Knop, Gerhard Roehrle
In a paper from 2015, we determined all spherical affine homogeneous varieties for simple algebraic groups in arbitrary characteristic. The present paper extends this classificatio…
Restricting invariants of unitary reflection groups
Nils Amend, Angela Berardinelli, J. Matthew Douglass +1
Suppose that G is a finite, unitary reflection group acting on a complex vector space V and X is the fixed point subspace of an element of G. Define N to be the setwise stabilizer…
Computations for Coxeter arrangements and Solomon's descent algebra III: Groups of rank seven and eight
Marcus Bishop, J. Matthew Douglass, Goetz Pfeiffer +1
In this paper we extend the computations in parts I and II of this series of papers and complete the proof of a conjecture of Lehrer and Solomon expressing the character of a finit…
An Inductive Approach to Coxeter Arrangements and Solomon's Descent Algebra
J. Matthew Douglass, Goetz Pfeiffer, Gerhard Roehrle
In a recent paper we claimed that both the group algebra of a finite Coxeter group as well as the Orlik-Solomon algebra of can be decomposed into a sum of induced one-dimen…
The homology of the Steinberg variety and Weyl group coinvariants
J. Matthew Douglass, Gerhard Roehrle
Let G be a complex, connected, reductive algebraic group with Weyl group W and Steinberg variety Z. We show that the graded Borel-Moore homology of Z is isomorphic to the smash pro…