Browsing 1 - Oberwolfach Preprints (OWP) by Author "Röhrle, Gerhard"

Now showing items 1-14 of 14

Calculating conjugacy classes in Sylow p-subgroups of finite Chevalley groups of rank six and seven

[OWP-2013-10] Goodwin, Simon M.; Mosch, Peter; Röhrle, Gerhard (Mathematisches Forschungsinstitut Oberwolfach, 2013-04-10)

Let $G(q)$ be a finite Chevalley group, where $q$ is a power of a good prime $p$ , and let $U(q)$ be a Sylow $p$ -subgroup of $G(q)$ . Then a generalized version of a conjecture of Higman asserts that the number $k(U(q))$ of ...
Cocharacter-closure and spherical buildings

[OWP-2015-12] Bate, Michael; Herpel, Sebastian; Martin, Benjamin; Röhrle, Gerhard (Mathematisches Forschungsinstitut Oberwolfach, 2015-07-29)

Let $k$ be a field, let $G$ be a reductive $k$ -group and $V$ an affine $k$ -variety on which $G$ acts. In this note we continue our study of the notion of cocharacter-closed $G(k)$ -orbits in $V$ . In earlier work we used a ...
Cocharacter-Closure and the Rational Hilbert-Mumford Theorem

[OWP-2014-16] Bate, Michael; Herpel, Sebastian; Martin, Benjamin; Röhrle, Gerhard (Mathematisches Forschungsinstitut Oberwolfach, 2014-12-20)

For a field $k$ , let $G$ be a reductive $k$ -group and $V$ an affine $k$ -variety on which $G$ acts. Using the notion of cocharacter-closed $G(k)$ -orbits in $V$ , we prove a rational version of the celebrated Hilbert-Mumford ...
Edifices: Building-like Spaces Associated to Linear Algebraic Groups; In memory of Jacques Tits

[OWP-2023-04] Bate, Michael; Martin, Benjamin; Röhrle, Gerhard (Mathematisches Forschungsinstitut Oberwolfach, 2023-06-19)

Given a semisimple linear algebraic $k$ -group $G$ , one has a spherical building $Δ_G$ , and one can interpret the geometric realisation $Δ_G(\mathbb R)$ of $Δ_G$ in terms of cocharacters of $G$ . The aim of this paper is to ...
Flag-Accurate Arrangements

[OWP-2023-01] Mücksch, Paul; Röhrle, Gerhard; Tran, Tan Nhat (Mathematisches Forschungsinstitut Oberwolfach, 2023-02-13)

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 property of accuracy stems from a flag of flats ...
Freeness of Multi-Reflection Arrangements via Primitive Vector Fields

[OWP-2017-10] Hoge, Torsten; Mano, Toshiyuki; Röhrle, Gerhard; Stump, Christian (Mathematisches Forschungsinstitut Oberwolfach, 2017-04-20)

In 2002, Terao showed that every reflection multi-arrangement of a real reflection group with constant multiplicity is free by providing a basis of the module of derivations. We first generalize Terao's result to ...
G-complete reducibility in non-connected groups

[OWP-2013-09] Bate, Michael; Herpel, Sebastian; Martin, Benjamin; Röhrle, Gerhard (Mathematisches Forschungsinstitut Oberwolfach, 2013-04-10)

In this paper we present an algorithm for determining whether a subgroup $H$ of a non-connected reductive group $G$ is $G$ -completely reducible. The algorithm consists of a series of reductions; at each step, we perform ...
An inductive approach to coxeter arrangements and solomon's descent algebra

[OWP-2011-16] Douglass, J. Matthew; Pfeiffer, Götz; Röhrle, Gerhard (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-17)

In our recent paper [3], we claimed that both the group algebra of a finite Coxeter group W as well as the Orlik-Solomon algebra of W can be decomposed into a sum of induced one-dimensional representations of centralizers, ...
Inductive Freeness of Ziegler’s Canonical Multiderivations for Reflection Arrangements

[OWP-2017-14] Hoge, Torsten; Röhrle, Gerhard (Mathematisches Forschungsinstitut Oberwolfach, 2017-04-30)

Let $A$ be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction $A''$ of $A$ to any hyperplane endowed with the natural multiplicity is then a free multiarrangement. We initiate a study of the stronger ...
On commuting varieties of nilradicals of Borel subalgebras of reductive Lie algebras

[OWP-2012-14] Goodwin, Simon M.; Röhrle, Gerhard (Mathematisches Forschungsinstitut Oberwolfach, 2012-12-04)

Let $G$ be a connected reductive algebraic group defined over an algebraically closed field $\mathbb{k}$ of characteristic zero. We consider the commuting variety $\mathcal{C}(\mathfrak{u})$ of the nilradical $\mathfrak{u}$ ...
On Overgroups of Distinguished Unipotent Elements in Reductive Groups and Finite Groups of Lie Type

[OWP-2024-05] Bate, Michael; Böhm, Sören; Martin, Benjamin; Röhrle, Gerhard (Mathematisches Forschungsinstitut Oberwolfach, 2024-06-18)

Suppose G is a simple algebraic group defined over an algebraically closed field of good characteristic p. In 2018 Korhonen showed that if H is a connected reductive subgroup of G which contains a distinguished unipotent ...
On the Invariants of the Cohomology of Complements of Coxeter Arrangements

[OWP-2018-21] Douglass, J. Matthew; Pfeiffer, Götz; Röhrle, Gerhard (Mathematisches Forschungsinstitut Oberwolfach, 2018-10-22)

We refine Brieskorn's study of the cohomology of the complement of the reflection arrangement of a finite Coxeter group W. As a result we complete the verification of a conjecture by Felder and Veselov that gives an explicit ...
On Unipotent Radicals of Pseudo-Reductive Groups

[OWP-2017-12] Bate, Michael; Martin, Benjamin; Röhrle, Gerhard; Stewart, David I. (Mathematisches Forschungsinstitut Oberwolfach, 2017-04-27)

We establish some results on the structure of the geometric unipotent radicals of pseudo-reductive k-groups. In particular, let $k'$ be a purely inseparable field extension of k of degree $p^e$ and let $G$ denote the ...
The Subgroup Structure of Pseudo-Reductive Groups

[OWP-2024-08] Bate, Michael; Martin, Benjamin; Röhrle, Gerhard; Sercombe, Damian (Mathematisches Forschungsinstitut Oberwolfach, 2024-07-31)

Let $k$ be a field. We investigate the relationship between subgroups of a pseudo-reductive $k$ -group $G$ and its maximal reductive quotient $G'$ , with applications to the subgroup structure of $G$ . Let $k'/k$ be the minimal ...

Browsing 1 - Oberwolfach Preprints (OWP) by Author "Röhrle, Gerhard"

Calculating conjugacy classes in Sylow p-subgroups of finite Chevalley groups of rank six and seven ﻿

Cocharacter-closure and spherical buildings ﻿

Cocharacter-Closure and the Rational Hilbert-Mumford Theorem ﻿

Edifices: Building-like Spaces Associated to Linear Algebraic Groups; In memory of Jacques Tits ﻿

Flag-Accurate Arrangements ﻿

Freeness of Multi-Reflection Arrangements via Primitive Vector Fields ﻿

G-complete reducibility in non-connected groups ﻿

An inductive approach to coxeter arrangements and solomon's descent algebra ﻿

Inductive Freeness of Ziegler’s Canonical Multiderivations for Reflection Arrangements ﻿

On commuting varieties of nilradicals of Borel subalgebras of reductive Lie algebras ﻿

On Overgroups of Distinguished Unipotent Elements in Reductive Groups and Finite Groups of Lie Type ﻿

On the Invariants of the Cohomology of Complements of Coxeter Arrangements ﻿

On Unipotent Radicals of Pseudo-Reductive Groups ﻿

The Subgroup Structure of Pseudo-Reductive Groups ﻿

Calculating conjugacy classes in Sylow p-subgroups of finite Chevalley groups of rank six and seven

Cocharacter-closure and spherical buildings

Cocharacter-Closure and the Rational Hilbert-Mumford Theorem

Edifices: Building-like Spaces Associated to Linear Algebraic Groups; In memory of Jacques Tits

Flag-Accurate Arrangements

Freeness of Multi-Reflection Arrangements via Primitive Vector Fields

G-complete reducibility in non-connected groups

An inductive approach to coxeter arrangements and solomon's descent algebra

Inductive Freeness of Ziegler’s Canonical Multiderivations for Reflection Arrangements

On commuting varieties of nilradicals of Borel subalgebras of reductive Lie algebras

On Overgroups of Distinguished Unipotent Elements in Reductive Groups and Finite Groups of Lie Type

On the Invariants of the Cohomology of Complements of Coxeter Arrangements

On Unipotent Radicals of Pseudo-Reductive Groups

The Subgroup Structure of Pseudo-Reductive Groups