EXISTENCE OF LATTICES IN KAC–MOODY GROUPS OVER FINITE FIELDS
EXISTENCE OF LATTICES IN KAC–MOODY GROUPS OVER FINITE FIELDS
复制标题
有限域上KAC-穆迪群中格的存在性
DOI：
10.1142/s0219199703001117
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发表时间：
2003
影响因子：
1.6
通讯作者：
H. Garland
中科院分区：
文献类型：
--
作者：
Lisa Carbone;H. Garland
设为Kac-Moody李代数。我们用的表示理论解释了Tits的伴随群函子，并构造了有限域k上的局部紧的“Kac-Moody群”.利用(孪生)BN-对(G，B，N)和(G，B-，N)，我们证明了如果k“足够大”，我们还构造了一个由秩为2的一致格和非一致格组成的不可数无穷族。我们猜想，它们构成了G中无数不同的不同共轭类。构造秩为2的非一致格的基本工具是G的球面Tits系统。
Let be a Kac–Moody Lie algebra. We give an interpretation of Tits' associated group functor using representation theory of and we construct a locally compact "Kac–Moody group" G over a finite field k. Using (twin) BN-pairs (G,B,N) and (G,B-,N) for G we show that if k is "sufficiently large", then the subgroup B- is a non-uniform lattice in G. We have also constructed an uncountably infinite family of both uniform and non-uniform lattices in rank 2. We conjecture that these form uncountably many distinct conjugacy classes in G. The basic tool for the construction of non-uniform lattices in rank 2 is a spherical Tits system for G which we also construct.