Abstract.
In this paper, we identify the greatest common quotient (GCQ) of the Borel-Serre compactification and the toroidal compactifications of Hermitian locally symmetric spaces with a new compactification. Using this compactification, we completely settle a conjecture of Harris-Zucker that this GCQ is equal to the Baily-Borel compactification. We also show that the GCQ of the reductive Borel-Serre compactification and the toroidal compactifications is the Baily-Borel compactification. There are two key ingredients in the proof: ergodicity of certain adjoint action on nilmanifolds and incompatibility between the ambient linear structure and the intrinsic Riemannian structure of homothety sections of symmetric cones.
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Submitted: July 1997, revised version: March 1998
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Ji, L. The Greatest Common Quotient of Borel-Serre and the Toroidal Compactifications of Locally Symmetric Spaces. GAFA, Geom. funct. anal. 8, 978–1015 (1998). https://doi.org/10.1007/s000390050121
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DOI: https://doi.org/10.1007/s000390050121