• 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 ΔG, and one can interpret the geometric realisation ΔG(R) of ΔG 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 k of characteristic zero. We consider the commuting variety C(u) of the nilradical 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 pe 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 ...