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Existence of non-obvious divergent trajectories in homogeneous spaces

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Abstract

We prove a modified version for a conjecture of Weiss from 2004. Let G be a semisimple real algebraic group defined over ℚ, Γ be an arithmetic subgroup of G. A trajectory in G/Γ is divergent if eventually it leaves every compact subset, and is obvious divergent if there is a finite collection of algebraic data which cause the divergence. Let A be a diagonalizable subgroup of G of positive dimension. We show that if the projection of A to any ℚ-factor of G is of small enough dimension (relatively to the ℚ-rank of the ℚ-factor), then there are non-obvious divergent trajectories for the action of A on G/Γ.

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  1. Mathematics Department, UC San Diego, 9500 Gilman Dr, La Jolla, San Diego, CA, 92093, USA

    Nattalie Tamam

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  1. Nattalie Tamam
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Correspondence to Nattalie Tamam.

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Tamam, N. Existence of non-obvious divergent trajectories in homogeneous spaces. Isr. J. Math. 247, 459–478 (2022). https://doi.org/10.1007/s11856-021-2274-2

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  • DOI: https://doi.org/10.1007/s11856-021-2274-2

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