4 citations · 5 across the 11 of their papers we have counts for
17 papers
Parabolic Normalizers in Finite Coxeter Groups as Subdirect Products
J. Matthew Douglass, Götz Pfeiffer, Gerhard Roehrle
We revisit the structure of the normalizer of a parabolic subgroup in a finite Coxeter group , originally described by Howlett. Building on Howlett's Lemma, which p…
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…
The Leray-Hirsch Theorem for equivariant oriented cohomology of flag varieties
J. Matthew Douglass, Changlong Zhong
We use the formal affine Demazure algebra to construct an explicit Leray-Hirsch Theorem for torus equivariant oriented cohomology of flag varieties. We then generalize the Borel mo…
On the Invariants of the Cohomology of Complements of Coxeter Arrangements
J. Matthew Douglass, Goetz Pfeiffer, Gerhard Roehrle
We refine Brieskorn's study of the cohomology of the complement of the reflection arrangement of a finite Coxeter group . As a result we complete the verification of a conjectur…
A decomposition of the group algebra of a hyperoctahedral group
J. Matthew Douglass, Drew E. Tomlin
The descent algebra of a finite Coxeter group W is a subalgebra of the group algebra defined by Solomon. Descent algebras of symmetric groups have properties that are not shared by…
Modules for Yokonuma-type Hecke algebras
Ojas Dave, J. Matthew Douglass
This paper describes the module categories for a family of generic Hecke algebras that specialize to the complex reflection groups G(r,1,n) and to the certain endomorphism rings of…
Schur-Weyl duality and the free Lie algebra
Stephen Doty, J. Matthew Douglass
We prove an analogue of Schur-Weyl duality for the space of homogeneous Lie polynomials of degree r in n variables.
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…
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…
On reflection subgroups of finite Coxeter groups
J. Matthew Douglass, Goetz Pfeiffer, Gerhard Roehrle
Let be a finite Coxeter group. We classify the reflection subgroups of up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection…
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…
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…
Generic Hecke Algebras for Monomial Groups
S. I. Alhaddad, J. M. Douglass
In this paper we define a two-variable, generic Hecke algebra, H, for each complex reflection group G(b,1,n). The algebra H specializes to the group algebra of G(b,1,n) and also to…