Browsing 1 - Oberwolfach Preprints (OWP) by MSC "20"
Now showing items 21-40 of 44
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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 ... -
Invariant Four-forms and Symmetric Pairs
[OWP-2012-03] (Mathematisches Forschungsinstitut Oberwolfach, 2012-04-24)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
[OWP-2017-15] (Mathematisches Forschungsinstitut Oberwolfach, 2017-05-24)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
[OWP-2018-13] (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-01)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
[OWP-2011-18] (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
[OWP-2019-08] (Mathematisches Forschungsinstitut Oberwolfach, 2019-03-01)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 ... -
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 Generalizations of Kac-Moody Groups
[OWP-2010-06] (Mathematisches Forschungsinstitut Oberwolfach, 2010-03-10)In [7] we define a Curtis-Tits group as a certain generalization of a Kac-Moody group. We distinguish between orientable and non-orientable Curtis-Tits groups and identify all orientable Curtis-Tits groups as Kac-Moody ... -
On Residuals of Finite Groups
[OWP-2019-17] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-28)A theorem of Dolfi, Herzog, Kaplan, and Lev [DHKL07, Thm. C] asserts that in a finite group with trivial Fitting subgroup, the size of the soluble residual of the group is bounded from below by a certain power of the group ... -
On the Complement of the Richardson Orbit
[OWP-2010-09] (Mathematisches Forschungsinstitut Oberwolfach, 2010-03-13)We consider parabolic subgroups of a general algebraic group over an algebraically closed field $k$ whose Levi part has exactly $t$ factors. By a classical theorem of Richardson, the nilradical of a parabolic subgroup $P$ ... -
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 ... -
Plethysms, replicated Schur functions and series, with applications to vertex operators
[OWP-2010-12] (Mathematisches Forschungsinstitut Oberwolfach, 2010-03-14)Specializations of Schur functions are exploited to define and evaluate the Schur functions $s_\lambda [\alpha X]$ and plethysms $s_\lambda [\alpha s_\nu(X))]$ for any $\alpha$-integer, real or complex. Plethysms are then ... -
Products of pairs of Dehn twists and maximal real Lefschetz fibrations
[OWP-2011-32] (Mathematisches Forschungsinstitut Oberwolfach, 2011)We address the problem of existence and uniqueness of a factorization of a given element of the modular group into a product of two Dehn twists. As a geometric application, we conclude that any maximal real elliptic ... -
Reducing sub-modules of the Bergman module $\mathbb A^{(\lambda)}(\mathbb D^n)$ under the action of the symmetric group
[OWP-2017-19] (Mathematisches Forschungsinstitut Oberwolfach, 2017-07-20)The weighted Bergman spaces on the polydisc, $\mathbb A^{(\lambda)}(\mathbb D^n)$, $\lambda>0,$ splits into orthogonal direct sum of subspaces $\mathbb P_{\boldsymbol p}\big(\mathbb A^{(\lambda)}(\mathbb D^n)\big)$ indexed ... -
The Simplicial Complex of Brauer Pairs of a Finite Reductive Group
[OWP-2023-12] (Mathematisches Forschungsinstitut Oberwolfach, 2023-07-17)In this paper we study the simplicial complex induced by the poset of Brauer pairs ordered by inclusion for the family of finite reductive groups. In the defining characteristic case the homotopy type of this simplicial ... -
Supertropical linear algebra
[OWP-2010-14] (Mathematisches Forschungsinstitut Oberwolfach, 2010)The objective of this paper is to lay out the algebraic theory of supertropical vector spaces and linear algebra, utilizing the key antisymmetric relation of "ghost surpasses." Special attention is paid to the various ... -
Torsion-free Covers of Solvable Minimax Groups
[OWP-2015-15] (Mathematisches Forschungsinstitut Oberwolfach, 2015-11-18)We prove that every finitely generated solvable minimax group can be realized as a quotient of a torsion-free solvable minimax group. This result has an application to the investigation of random walks on finitely generated ... -
Trivial Source Character Tables of SL2(q)
[OWP-2022-02] (Mathematisches Forschungsinstitut Oberwolfach, 2022-01-28)We compute the trivial source character tables (also called species tables of the trivial source ring) of the infinite family of finite groups SL(2,q) over a large enough field of positive characteristic $\ell$ via ...