Zobrazeno 1 - 10
of 295
pro vyhledávání: '"Röhrle, Gerhard"'
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 element $u$ of $G$ of
Externí odkaz:
http://arxiv.org/abs/2407.16379
Cuntz and K\"uhne introduced the class of connected subgraph arrangements $A_G$, depending on a graph $G$, and classified all graphs $G$ such that the corresponding arrangement $A_G$ is free. We extend their result to the multiarrangement case and cl
Externí odkaz:
http://arxiv.org/abs/2406.19866
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 field of definition for t
Externí odkaz:
http://arxiv.org/abs/2406.11286
Let $H \subseteq G$ be connected reductive linear algebraic groups defined over an algebraically closed field of characteristic $p> 0$. In our first main theorem we show that if a closed subgroup $K$ of $H$ is $H$-completely reducible, then it is als
Externí odkaz:
http://arxiv.org/abs/2401.16927
Publikováno v:
Innov. Incidence Geom. 20 (2023), no. 2--3, 79--134
Given a semisimple linear algebraic $k$-group $G$, one has a spherical building $\Delta_G$, and one can interpret the geometric realisation $\Delta_G(\mathbb R)$ of $\Delta_G$ in terms of cocharacters of $G$. The aim of this paper is to extend this c
Externí odkaz:
http://arxiv.org/abs/2305.11770
Publikováno v:
Eur. J. Math. 9 (2023), no. 4, Paper No. 116, 27 pp
Let $G$ be a connected reductive linear algebraic group over a field $k$. Using ideas from geometric invariant theory, we study the notion of $G$-complete reducibility over $k$ for a Lie subalgebra $\mathfrak h$ of the Lie algebra $\mathfrak g = Lie(
Externí odkaz:
http://arxiv.org/abs/2305.00841
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 in the intersection lattice o
Externí odkaz:
http://arxiv.org/abs/2302.00343
Let $\mathcal A$ be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction $\mathcal A"$ of $\mathcal A$ to any hyperplane endowed with the natural multiplicity $\kappa$ is then a free multiarrangement. In 2024, the first two aut
Externí odkaz:
http://arxiv.org/abs/2210.00436
We describe a straightforward construction of the pseudo-split absolutely pseudo-simple groups of minimal type with irreducible root systems of type $BC_n$; these exist only in characteristic $2$. We also give a formula for the dimensions of their ir
Externí odkaz:
http://arxiv.org/abs/2205.00800
Autor:
Hoge, Torsten, Roehrle, Gerhard
Let $\mathcal A$ be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction $\mathcal A''$ of $\mathcal A$ to any hyperplane endowed with the natural multiplicity $\kappa$ is then a free multiarrangement $(\mathcal A'',\kappa)$. T
Externí odkaz:
http://arxiv.org/abs/2204.09540