Browsing by MSC "20"
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Calculating conjugacy classes in Sylow psubgroups of finite Chevalley groups of rank six and seven
[OWP201310] (Mathematisches Forschungsinstitut Oberwolfach, 20130410)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 ... 
Cataland: Why the Fuß?
[OWP201901] (Mathematisches Forschungsinstitut Oberwolfach, 20190121)The three main objects in noncrossing Catalan combinatorics associated to a finite Coxeter system are noncrossing partitions, clusters, and sortable elements. The first two of these have known FußCatalan generalizations. ... 
Categoric Aspects of Authentication
[OWP201205] (Mathematisches Forschungsinstitut Oberwolfach, 20120424) 
Cocharacterclosure and spherical buildings
[OWP201512] (Mathematisches Forschungsinstitut Oberwolfach, 20150729)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 cocharacterclosed $G(k)$orbits in $V$. In earlier work we used a ... 
CocharacterClosure and the Rational HilbertMumford Theorem
[OWP201416] (Mathematisches Forschungsinstitut Oberwolfach, 20141220)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 cocharacterclosed $G(k)$orbits in $V$ , we prove a rational version of the celebrated HilbertMumford ... 
Computing Congruence Quotients of Zariski Dense Subgroups
[OWP201822] (Mathematisches Forschungsinstitut Oberwolfach, 20181026)We obtain a computational realization of the strong approximation theorem. That is, we develop algorithms to compute all congruence quotients modulo rational primes of a finitely generated Zariski dense group $H \leq ... 
Congruences Associated with Families of Nilpotent Subgroups and a Theorem of Hirsch
[OWP201916] (Mathematisches Forschungsinstitut Oberwolfach, 20190527)Our main result associates a family of congruences with each suitable system of nilpotent subgroups of a finite group. Using this result, we complete and correct the proof of a theorem of Hirsch concerning the class number ... 
A construction of hyperbolic Coxeter groups
[OWP201004] (Mathematisches Forschungsinstitut Oberwolfach, 2010)We give a simple construction of Gromov hyperbolic Coxeter groups of arbitrarily large virtual cohomological dimension. Our construction provides new examples of such groups. Using this one can construct e.g. new groups ... 
Experimenting with Symplectic Hypergeometric Monodromy Groups
[OWP201915] (Mathematisches Forschungsinstitut Oberwolfach, 20190522)We present new computational results for symplectic monodromy groups of hypergeometric differential equations. In particular, we compute the arithmetic closure of each group, sometimes justifying arithmeticity. The results ... 
Experimenting with Zariski Dense Subgroups
[OWP201731] (Mathematisches Forschungsinstitut Oberwolfach, 20171028)We give a method to describe all congruence images of a finitely generated Zariski dense group $H\leq SL(n, \mathbb{R})$. The method is applied to obtain efficient algorithms for solving this problem in odd prime degree ... 
Freeness of MultiReflection Arrangements via Primitive Vector Fields
[OWP201710] (Mathematisches Forschungsinstitut Oberwolfach, 20170420)In 2002, Terao showed that every reflection multiarrangement 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 ... 
Gcomplete reducibility in nonconnected groups
[OWP201309] (Mathematisches Forschungsinstitut Oberwolfach, 20130410)In this paper we present an algorithm for determining whether a subgroup $H$ of a nonconnected reductive group $G$ is $G$completely reducible. The algorithm consists of a series of reductions; at each step, we perform ... 
Ghost Algebras of Double Burnside Algebras via Schur Functors
[OWP201209] (Mathematisches Forschungsinstitut Oberwolfach, 20120703)For a finite group $G$, we introduce a multiplication on the $\mathbb{Q}$vector space with basis $\mathscr{S}_{G\times G}$, the set of subgroups of ${G \times G}$. The resulting $\mathbb{Q}$algebra $\tilde{A}$ can be ... 
An inductive approach to coxeter arrangements and solomon's descent algebra
[OWP201116] (Mathematisches Forschungsinstitut Oberwolfach, 20110517)In our recent paper [3], we claimed that both the group algebra of a finite Coxeter group W as well as the OrlikSolomon algebra of W can be decomposed into a sum of induced onedimensional representations of centralizers, ... 
Inductive Freeness of Ziegler’s Canonical Multiderivations for Reflection Arrangements
[OWP201714] (Mathematisches Forschungsinstitut Oberwolfach, 20170430)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 ... 
Invariant Fourforms and Symmetric Pairs
[OWP201203] (Mathematisches Forschungsinstitut Oberwolfach, 20120424)We give criteria for real, complex and quaternionic representations to define $s$representations, focusing on exceptional Lie algebras defined by spin representations. As applications, we obtain the classification of ... 
Linear Syzygies, Hyperbolic Coxeter Groups and Regularity
[OWP201715] (Mathematisches Forschungsinstitut Oberwolfach, 20170524)We build a new bridge between geometric group theory and commutative algebra by showing that the virtual cohomological dimension of a Coxeter group is essentially the regularity of the Stanley–Reisner ring of its nerve. ... 
The Magic Square of Reflections and Rotations
[OWP201813] (Mathematisches Forschungsinstitut Oberwolfach, 20180701)We show how Coxeter’s work implies a bijection between complex reflection groups of rank two and real reflection groups in 0(3). We also consider this magic square of reflections and rotations in the framework of Clifford ... 
New representations of matroids and generalizations
[OWP201118] (Mathematisches Forschungsinstitut Oberwolfach, 2011)We extend the notion of matroid representations by matrices over fields by considering new representations of matroids by matrices over finite semirings, more precisely over the boolean and the superboolean semirings. This ... 
On a Group Functor Describing Invariants of Algebraic Surfaces
[OWP201908] (Mathematisches Forschungsinstitut Oberwolfach, 20190301)Liedtke (2008) has introduced group functors $K$ and $\tilde K$, which are used in the context of describing certain invariants for complex algebraic surfaces. He proved that these functors are connected to the theory of ...