高阶几乎极小非一致格
Almost-minimal nonuniform lattices of higher rank
摘要：
若Gamma是实秩大于1的半单李群中的一个非一致不可约格，我们证明了Gamma包含一个子群同构于SL（3，R），SL（3，C），或直积SL（2，R）^m x SL（2，C）^n$中的一个非一致不可约格，其中m + n > 1. (In几何术语，这可以解释为关于有限体积的、非紧的、局部对称的高阶空间的全测地子空间的存在性的陈述。结果的另一种表述是，如果G是Q（有理数）上的任何迷向的几乎单代数群，使得G的实秩大于1，则G包含迷向的几乎单Q-子群H，使得H是拟分裂的，并且H的实秩大于1。
英文摘要：
If Gamma is a nonuniform, irreducible lattice in a semisimple Lie group whose real rank is greater than 1, we show Gamma contains a subgroup that is isomorphic to a nonuniform, irreducible lattice in either SL(3,R), SL(3,C), or a direct product SL(2,R)^m x SL(2,C)^n$, with m + n > 1. (In geometric terms, this can be interpreted as a statement about the existence of totally geodesic subspaces of finite-volume, noncompact, locally symmetric spaces of higher rank.) Another formulation of the result states that if G is any isotropic, almost simple algebraic group over Q (the rational numbers), such that the real rank of G is greater than 1, then G contains an isotropic, almost simple Q-subgroup H, such that H is quasisplit, and the real rank of H is greater than 1.
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