# Hyperbolic Weyl groups and the four normed division algebras

@article{Feingold2008HyperbolicWG, title={Hyperbolic Weyl groups and the four normed division algebras}, author={Alex J. Feingold and Axel Kleinschmidt and Hermann Nicolai}, journal={Journal of Algebra}, year={2008}, volume={322}, pages={1295-1339} }

## 22 Citations

### Modular realizations of hyperbolic Weyl groups

- Mathematics
- 2010

We study the recently discovered isomorphisms between hyperbolic Weyl groups and modular groups over integer domains in normed division algebras. We show how to realize the group action via…

### On Fundamental Domains and Volumes of Hyperbolic Coxeter–Weyl Groups

- Mathematics
- 2012

We present a simple method for determining the shape of fundamental domains of generalized modular groups related to Weyl groups of hyperbolic Kac–Moody algebras. These domains are given as subsets…

### On Fundamental Domains and Volumes of Hyperbolic Coxeter–Weyl Groups

- MathematicsLetters in Mathematical Physics
- 2011

We present a simple method for determining the shape of fundamental domains of generalized modular groups related to Weyl groups of hyperbolic Kac–Moody algebras. These domains are given as subsets…

### 2-roots for simply laced Weyl groups

- Mathematics
- 2022

. We introduce and study “2-roots”, which are symmetrized tensor products of orthogonal roots of Kac–Moody algebras. We concentrate on the case where W is the Weyl group of a simply laced Y-shaped…

### Simply-laced isomonodromy systems

- Mathematics
- 2011

A new class of isomonodromy equations will be introduced and shown to admit Kac–Moody Weyl group symmetries. This puts into a general context some results of Okamoto on the 4th, 5th and 6th Painlevé…

### Simply-laced isomonodromy systems

- MathematicsPublications mathématiques de l'IHÉS
- 2012

A new class of isomonodromy equations will be introduced and shown to admit Kac–Moody Weyl group symmetries. This puts into a general context some results of Okamoto on the 4th, 5th and 6th Painlevé…

### Irregular connections and Kac-Moody root systems

- Mathematics
- 2008

Some moduli spaces of irregular connections on the trivial bundle over the Riemann sphere will be identified with Nakajima quiver varieties. In particular this enables us to associate a Kac-Moody…

### AUTOMORPHIC CORRECTION OF THE HYPERBOLIC KAC-MOODY ALGEBRA E10

- Mathematics
- 2013

In this paper, we study automorphic correction of the hyperbolic Kac-Moody algebra E10, using the Borcherds product for O(10, 2) attached to a weakly holomorphic modular form of weight −4 for SL2(Z).…

### Spin covers of maximal compact subgroups of Kac-Moody groups and of Weyl groups

- Mathematics
- 2015

The maximal compact subgroup SO(\(n\),ℝ) of SL(\(n\),ℝ) admits two double covers Spin (\(n\),ℝ) and O(\(n\),ℝ). In this thesis we show that in fact given any simply-laced diagram ∆, with associated…

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