Discrete automorphism groups of convex cones of finite type
Discrete automorphism groups of convex cones of finite type
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DOI：
10.1112/s0010437x14007404
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发表时间：
2009-08
影响因子：
1.8
通讯作者：
E. Looijenga
中科院分区：
文献类型：
--
作者：
E. Looijenga
摘要 我们研究了 $\text{SL}(n,\mathbb{Z})$ 的子群，它们在 $\mathbb{R}^{n}$ 中保留了一个开放的非退化凸锥体，并在该锥体中承认一个多面体锥体作为基本域，其中允许一些面位于边界上。例子是作用于自对偶锥体的算术群、某些 Kac-Moody 代数的 Weyl 群，它们确实出现在代数几何中，作为作用于其大锥体的射影流形的自同构群。
Abstract 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.