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Discrete automorphism groups of convex cones of finite type

Part of: Other groups of matrices Discrete geometry

Published online by Cambridge University Press:  10 September 2014

Eduard Looijenga
Eduard Looijenga*
Affiliation:
Mathematical Sciences Center, Jin Chun Yuan West Building, Tsinghua University, Haidan District, Beijing 100084, PR China email Eduard@math.tsinghua.edu.cn
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Abstract

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We investigate subgroups of $\text{SL}(n,\mathbb{Z})$ which preserve an open nondegenerate convex cone in $\mathbb{R}^{n}$ and admit in that cone as fundamental domain a polyhedral cone of which some faces are allowed to lie on the boundary. Examples are arithmetic groups acting on self-dual cones, Weyl groups of certain Kac–Moody algebras, and they do occur in algebraic geometry as the automorphism groups of projective manifolds acting on their ample cones.

Keywords

convex conearithmetic group

MSC classification

Primary: 52C07: Lattices and convex bodies in $n$ dimensions
Secondary: 20H05: Unimodular groups, congruence subgroups
Type
Research Article
Information
Compositio Mathematica , Volume 150 , Issue 11 , November 2014 , pp. 1939 - 1962
Copyright
© The Author 2014 

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