Now showing items 1-7 of 7

• #### Experimenting with Zariski Dense Subgroups ﻿

[OWP-2017-31] (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-28)
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 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 ...
• #### 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 ...
• #### 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. ...
• #### 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 ...
• #### 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 Varchenko Determinant of a Coxeter Arrangement ﻿

[OWP-2017-33] (Mathematisches Forschungsinstitut Oberwolfach, 2017-11-24)
The Varchenko determinant is the determinant of a matrix defined from an arrangement of hyperplanes. Varchenko proved that this determinant has a beautiful factorization. It is, however, not possible to use this factorization ...