arXiv subjects

Kay Paulus

Publications and source records attributed to Kay Paulus.

5 recordsLinked to original sources

arXiv2019

(Quasi-)Hamiltonian manifolds of cohomogeneity one

We classify compact, connected Hamiltonian and quasi-Hamiltonian manifolds of cohomogeneity one (which is the same as being multiplicity free of rank one). Here the group acting is a compact connected Lie group (simply connected in the quasi-Hamiltonian case). This work is a concretization of the more general classification (arXiv:1612.03843) of multiplicity free manifolds in the special case of rank one. As a result we obtain numerous new concrete examples of multiplicity free quasi-Hamiltonian manifolds or, equivalently, Hamiltonian loop group actions.

math.SG↗

arXiv2019

Quasi-Hamiltonian model spaces

Let K be a simple and simply connected compact Lie group. We call a (twisted) quasi-Hamiltonian K-manifold M a quasi-Hamiltonian model space if it is multiplicity free and its momentum map is surjective. We explicitly identify the subgroups of the Lie algebra of the maximal torus of K, which, by F. Knop's classification of multiplicity free quasi-Hamiltonian manifolds, are in one-to-one correspondence with the isomorphism classes of quasi-Hamiltonian model K-spaces.

math.RT↗

arXiv2018

Geometrische Konstruktionen und Origami

The aim of this article is to give practicing teachers an overview about the theory behind paperfolding, it is my qualifying thesis(Zulassungsarbeit) as a teacher in Germany. It is a survey about the relations between paperfolding and algebra, in particular Galois theory. We develop a system of fundamental foldings for paperfolding, discuss which field can be constructed using these techniques and advance to concrete constructions solving (classical) construction problems. Finally, we think about possible generalisations of the given system of fundamental constructions. Das Ziel dieser Arbeit ist es, aktiven Lehrern einen \"Uberblick \"uber die algebraische Theorie hinter Origami zu geben, der Artikel ist meine Zulassungsarbeit. Es handelt sich um einen \"Ubersichtsartikel \"uber die Relationen zwischen Origami und Algebra, insbesondere Galoistheorie. Wir entwickeln ein System von Grundkonstruktionen, diskutieren den K\"orper der mit Origami konstruierbaren Zahlen und wenden unser Wissen auf (klassische) Konstruktionsprobleme an. Zuletzt denken wir \"uber m\"ogliche Erweiterungen des gegebenen Systems fundamentaler Konstruktionen nach.

math.HO↗

arXiv2017

Momentum polytopes of rank one for multiplicity free quasi-Hamiltonian manifolds

We classify all momentum polytopes of rank one for multiplicity free quasi-Hamiltonian $K$-manifolds for simple and simply connected Lie groups $K$ by using the methods developed in a recent paper by F. Knop. This leads to lots of new concrete examples of multiplicity free quasi-Hamiltonian manifolds or equivalently, Hamiltonian loop group actions.

math.RT↗

arXiv2017

On some families of smooth affine spherical varieties of full rank

Let G be a complex connected reductive group. I. Losev has shown that a smooth affine spherical G-variety X is uniquely determined by its weight monoid, which is the set of irreducible representations of G that occur in the coordinate ring of X. In this paper we use a combinatorial characterization of the weight monoids of smooth affine spherical varieties to classify: (a) all such varieties when G is $\mathrm{SL}(2) \times \mathbb{C}^{\times}$ and (b) all such varieties for G simple which have a G-saturated weight monoid of full rank. We also use the characterization and F. Knop's classification theorem for multiplicity free Hamiltonian manifolds to give a new proof of C. Woodward's result that every reflective Delzant polytope is the moment polytope of such a manifold.

math.AG↗