Zobrazeno 1 - 10
of 241
pro vyhledávání: '"Bate, Michael"'
Autor:
Bate, Michael, Stewart, David I.
Let k be a field, let G be a smooth affine k-group and V a finite-dimensional G-module. We say V is \emph{rigid} if the socle series and radical series coincide for the action of G on each indecomposable summand of V; say V is \emph{geometrically rig
Externí odkaz:
http://arxiv.org/abs/2409.05221
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
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
We compute the homology of the matching complex $M(\Gamma)$, where $\Gamma$ is the complete hypergraph on $n\geq 2$ vertices, and analyse the $S_n$-representations carried by this homology. These results are achieved using standard techniques in comb
Externí odkaz:
http://arxiv.org/abs/2312.13750
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
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
Publikováno v:
Forum of Mathematics, Sigma 10 (2022) e13
We study reductive subgroups $H$ of a reductive linear algebraic group $G$ -- possibly non-connected -- such that $H$ contains a regular unipotent element of $G$. We show that under suitable hypotheses, such subgroups are $G$-irreducible in the sense
Externí odkaz:
http://arxiv.org/abs/2107.01925
Publikováno v:
Forum of Mathematics, Sigma 8 (2020) e43
Let $G$ be a reductive algebraic group---possibly non-connected---over a field $k$ and let $H$ be a subgroup of $G$. If $G= GL_n$ then there is a degeneration process for obtaining from $H$ a completely reducible subgroup $H'$ of $G$; one takes a lim
Externí odkaz:
http://arxiv.org/abs/2004.08105