Now showing items 1-11 of 11

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

[OWP-2013-10] (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] (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] (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 ...
• Flag-Accurate Arrangements ﻿

[OWP-2023-01] (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] (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] (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] (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] (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] (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 the Invariants of the Cohomology of Complements of Coxeter Arrangements ﻿

[OWP-2018-21] (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] (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 ...