9 citations · 39 across the 30 of their papers we have counts for
47 papers
Namikawa--Weyl groups of symplectic quotient singularities
Gwyn Bellamy, Gerhard Röhrle, Johannes Schmitt
We classify the Namikawa--Weyl groups associated to symplectic quotient singularities when is a symplectic reflection group. Our classification shows that every irreducib…
On Normalizers of Parabolic Subgroups of Quaternionic Reflection Groups
Gerhard Roehrle, Johannes Schmitt
By work of Howlett and Muraleedaran--Taylor, a parabolic subgroup of a real or complex reflection group always admits a complement in its normalizer. In this note, we investigate t…
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…
On connected subgraph arrangements
Lorenzo Giordani, Tilman Möller, Paul Mücksch +1
Recently, Cuntz and Kühne introduced a particular class of hyperplane arrangements stemming from a given graph , so called connected subgraph arrangements . In this note we…
On good subgroups, Springer maps, and overgroups of distinguished unipotent elements in reductive groups
Michael Bate, Sören Böhm, Benjamin Martin +1
Suppose is a simple algebraic group defined over an algebraically closed field of good characteristic . In 2018 Korhonen showed that if is a connected reductive subgroup…
Free multiderivations of connected subgraph arrangements
Paul Mücksch, Gerhard Roehrle, Sven Wiesner
Cuntz and Kühne introduced the class of connected subgraph arrangements , depending on a graph , and classified all graphs such that the corresponding arrangement …
-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…
Edifices: Building-like spaces associated to linear algebraic groups
Michael Bate, Benjamin Martin, Gerhard Roehrle
Given a semisimple linear algebraic -group , one has a spherical building , and one can interpret the geometric realisation of in terms of cochara…
Complete reducibility for Lie subalgebras and semisimplification
Michael Bate, Sören Böhm, Benjamin Martin +2
Let be a connected reductive linear algebraic group over a field . Using ideas from geometric invariant theory, we study the notion of -complete reducibility over for…
Flag-accurate arrangements
Paul Mücksch, Gerhard Roehrle, Tan Nhat Tran
In [MR21], the first two authors introduced the notion of an accurate arrangement, a particular notion of freeness. In this paper, we consider a special subclass, where the propert…
Inductive Freeness of Ziegler's Canonical Multiderivations for Restrictions of Reflection Arrangements
Torsten Hoge, Gerhard Roehrle, Sven Wiesner
Let be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction of to any hyperplane endowed with the natural multiplicit…
A construction of pseudo-reductive groups with non-reduced root system
Michael Bate, Gerhard Röhrle, Damian Sercombe +1
We describe a straightforward construction of the pseudo-split absolutely pseudo-simple groups of minimal type with irreducible root systems of type ; these exist only in cha…
Inductive Freeness of Ziegler's Canonical Multiderivations
Torsten Hoge, Gerhard Roehrle
Let be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction of to any hyperplane endowed with the natural multiplici…
On Formality and Combinatorial Formality for hyperplane arrangements
Tilman Möller, Paul Mücksch, Gerhard Roehrle
A hyperplane arrangement is called formal provided all linear dependencies among the defining forms of the hyperplanes are generated by ones corresponding to intersections of codim…
Overgroups of regular unipotent elements in reductive groups
Michael Bate, Ben Martin, Gerhard Roehrle
We study reductive subgroups of a reductive linear algebraic group -- possibly non-connected -- such that contains a regular unipotent element of . We show that unde…
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…
Complete reducibility: Variations on a theme of Serre
Maike Gruchot, Alastair Litterick, Gerhard Roehrle
In this note, we unify and extend various concepts in the area of -complete reducibility, where is a reductive algebraic group. By results of Serre and Bate--Martin--Röhrle,…
Accurate Arrangements
Paul Mücksch, Gerhard Roehrle
Let be a Coxeter arrangement of rank . In 1987 Orlik, Solomon and Terao conjectured that for every , the first exponents of -…
A Hodge filtration of logarithmic vector fields for well-generated complex reflection groups
Takuro Abe, Gerhard Röhrle, Christian Stump +1
Given an irreducible well-generated complex reflection group, we construct an explicit basis for the module of vector fields with logarithmic poles along its reflection arrangement…
The topology of arrangements of ideal type
Nils Amend, Gerhard Roehrle
In 1962, Fadell and Neuwirth showed that the configuration space of the braid arrangement is aspherical. Having generalized this to many real reflection groups, Brieskorn conjectur…
Arrangements of ideal type are inductively free
Michael Cuntz, Gerhard Roehrle, Anne Schauenburg
Extending earlier work by Sommers and Tymoczko, in 2016 Abe, Barakat, Cuntz, Hoge, and Terao established that each arrangement of ideal type stemming from…
On the -problem for restrictions of complex reflection arrangements
Nils Amend, Pierre Deligne, Gerhard Roehrle
Let be a complex reflection group, and the set of the mirrors of the complex reflections in . It is known that the complement $X({\mathscr A}(…
Inductive Freeness of Ziegler's Canonical Multiderivations for Reflection Arrangements
Torsten Hoge, Gerhard Roehrle
Let be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction of to any hyperplane endowed with the natural multiplicity is then a free multiarra…
On unipotent radicals of pseudo-reductive groups
Michael Bate, Benjamin Martin, Gerhard Roehrle +1
We establish some results on the structure of the geometric unipotent radicals of pseudo-reductive k-groups. In particular, our main theorem gives bounds on the nilpotency class of…