arXiv subjects

Guntram Hainke

Publications and source records attributed to Guntram Hainke.

3 recordsLinked to original sources

arXiv2015

Generalized spin representations

We introduce the notion of a generalized spin representation of the maximal compact subalgebra of a symmetrizable Kac-Moody algebra in order to show that, if defined over a formally real field, every such subalgebra has a non-trivial reductive finite-dimensional quotient. The appendix illustrates how to compute the isomorphism types of these quotients for the real $E_n$ series. In passing this provides an elementary way of determining the isomorphism types of the maximal compact subalgebras of the semisimple split real Lie algebras of types $E_6$, $E_7$, $E_8$.

math.RT↗

arXiv2011

Embeddings of algebraic groups in Kac-Moody groups

Let $k_1,k_2$ be two fields of characteristic 0. Let $G_1$ be a split semisimple algebraic group over $k_1$, $G_2$ a split Kac--Moody group over $k_2$ and $ϕ\colon G_1(k_1)\to G_2(k_2)$ an abstract embedding. We show that $\im ϕ$ is a bounded subgroup whenever $k_1$ is an algebraic extension of the rational numbers, while there are embeddings with unbounded image if $k_1$ has infinite transcendence degree over the rational numbers.

math.GR↗

arXiv2011

The isomorphism problem for almost split Kac-Moody groups

We consider the isomorphism problem for almost split Kac--Moody groups, which have been constructed by Rémy via Galois descent from split Kac-Moody groups as defined by Tits. We show that under certain technical assumptions, any isomorphism between two such groups must preserve the canonical subgroup structure, i.e. the twin root datum associated to these groups, which generalizes results of Caprace in the split case. An important technical tool we use is the existence of maximal split subgroups inside almost split Kac-Moody groups, which generalizes the corresponding result of Borel-Tits for reductive algebraic groups.

math.GR↗