Zobrazeno 1 - 10
of 310
pro vyhledávání: '"20G41"'
Autor:
Dijols, Sarah
Let $a$ be a real euclidean vector space of finite dimension and $\Sigma$ a root system in $a$ with a basis $\Delta$. Let $\Theta \subset \Delta$ and $M = M_{\Theta}$ be a standard Levi of a reductive group $G$ such that $a_{\Theta}$ $= a_M / a_G$. L
Externí odkaz:
http://arxiv.org/abs/2407.18817
Autor:
De Medts, Tom, Meulewaeter, Jeroen
We study simple Lie algebras generated by extremal elements, over arbitrary fields of arbitrary characteristic. We show: (1) If the extremal geometry contains lines, then the Lie algebra admits a $5 \times 5$-grading that can be parametrized by a cub
Externí odkaz:
http://arxiv.org/abs/2407.10672
Autor:
Shan, Yi
Up to isomorphism, there is a unique connected semisimple algebraic group over $\mathbb{Q}$ of Lie type $\mathrm{F}_{4}$, with compact real points and split over $\mathbb{Q}_{p}$ for all primes $p$. Let $\mathbf{F}_{4}$ be such a group. In this paper
Externí odkaz:
http://arxiv.org/abs/2407.05859
This document presents the solutions to the exercises in the book "Albert algebras over commutative rings" published by Cambridge University Press, 2024.
Comment: Approximately 300 pages
Comment: Approximately 300 pages
Externí odkaz:
http://arxiv.org/abs/2406.02933
Autor:
Chirvasitu, Alexandru
We show that the endomorphisms of a compact connected group that extend to endomorphisms of every compact overgroup are precisely the trivial one and the inner automorphisms; this is an analogue, for compact connected groups, of results due to Schupp
Externí odkaz:
http://arxiv.org/abs/2309.12791
Autor:
Hetz, Jonas
In order to tackle the problem of generically determining the character tables of the finite groups of Lie type $\mathbf{G}(q)$ associated to a connected reductive group $\mathbf{G}$ over $\overline{\mathbb F}_p$, Lusztig developed the theory of char
Externí odkaz:
http://arxiv.org/abs/2309.09915
Autor:
Zenteno, Adrian
The global Langlands conjecture for $\text{GL}_n$ over a number field $F$ predicts a correspondence between certain algebraic automorphic representations $\pi$ of $\text{GL}_n(\mathbb{A}_F)$ and certain families $\{ \rho_{\pi,\ell} \}_\ell$ of $n$-di
Externí odkaz:
http://arxiv.org/abs/2306.02493
Autor:
Gvozdevsky, Pavel
We prove that an element from the Chevalley group of type $E_6$ or $E_7$ over a polynomial ring with coefficients in a small-dimensional ring can be reduced to an element of certain proper subsystem subgroup by a bounded number of elementary root ele
Externí odkaz:
http://arxiv.org/abs/2305.17012
Let $G$ be a simple algebraic group of exceptional type over an algebraically closed field of characteristic $p > 0$. This paper continues a long-standing effort to classify the connected reductive subgroups of $G$. Having previously completed the cl
Externí odkaz:
http://arxiv.org/abs/2304.08388
Autor:
Chenevier, Gaëtan, Gan, Wee Teck
We classify the pairs of group morphisms $\Gamma \rightarrow {\rm Spin}(7)$ which are element conjugate but not globally conjugate. As an application, we study the case where $\Gamma$ is the Weil group of a $p$-adic local field, which is relevant to
Externí odkaz:
http://arxiv.org/abs/2303.15897