9 citations · 39 across the 30 of their papers we have counts for
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-complete reducibility and saturation
Michael Bate, Sören Böhm, Alastair Litterick +2
Let be connected reductive linear algebraic groups defined over an algebraically closed field of characteristic . In our first main theorem we show that if a…
Invariants and semi-invariants in the cohomology of the complement of a reflection arrangement
J. Matthew Douglass, Goetz Pfeiffer, Gerhard Roehrle
Suppose V is a finite dimensional, complex vector space, A is a finite set of codimension one subspaces of V, and G is a finite subgroup of the general linear group GL(V) that perm…
Equivariant K-theory of generalized Steinberg varieties
J. Matthew Douglass, Gerhard Roehrle
We describe the equivariant K-groups of a family of generalized Steinberg varieties that interpolates between the Steinberg variety of a reductive, complex algebraic group and its…
Computations for Coxeter arrangements and Solomon's descent algebra II: Groups of rank five and six
Marcus Bishop, J. Matthew Douglass, Goetz Pfeiffer +1
In recent papers we have refined a conjecture of Lehrer and Solomon expressing the character of a finite Coxeter group acting on the th graded component of its Orlik-Solomon…
Computations for Coxeter arrangements and Solomon's descent algebra: Groups of rank three and four
Marcus Bishop, J. Matthew Douglass, Goetz Pfeiffer +1
In recent papers we have refined a conjecture of Lehrer and Solomon expressing the characters of a finite Coxeter group afforded by the homogeneous components of its Orlik-Solo…
Cohomology of Coxeter arrangements and Solomon's descent algebra
J. Matthew Douglass, Goetz Pfeiffer, Gerhard Roehrle
We refine a conjecture by Lehrer and Solomon on the structure of the Orlik-Solomon algebra of a finite Coxeter group and relate it to the descent algebra of . As a result, w…
Invariants of reflection groups, arrangements, and normality of decomposition classes in Lie algebras
J. Matthew Douglass, Gerhard Roehrle
Suppose that W is a finite, unitary, reflection group acting on the complex vector space V and X is a subspace of V. Define N to be the setwise stabilizer of X in W, Z to be the po…
On 1-dimensional representations of finite W-algebras associated to simple Lie algebras of exceptional type
Simon M. Goodwin, Gerhard Roehrle, Glenn Ubly
We consider the finite -algebra $U(\g,e)$ associated to a nilpotent element $e \in \g$ in a simple complex Lie algebra $\g$ of exceptional type. Using presentations obtained thr…