Auflistung nach Autor "Röhrle, Gerhard"
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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 ...