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arXiv · 1310.2552

Invariant Vectors for Weak Endoscopic and Saito-Kurokawa Lifts to GSp(4)

Mirko Rösner
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Abstract

Let A be the adele ring over a totally real number field F. For cohomological cuspidal automorphic irreducible representations of GSp(4,A) coming from weak endoscopic or Saito-Kurokawa Lifts we determine the local invariant spaces under the first principal congruence subgroup at the non-archimedean places. For F=Q this gives rise to dimension formulas regarding certain subspaces of the inner cohomology of the genus two Shimura variety corresponding to the principal congruence subgroup level N=2. We prove the conjectures made by Bergström, Faber and van der Geer in a recent paper.

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Mirko Rösner. 2014-04-03. Invariant Vectors for Weak Endoscopic and Saito-Kurokawa Lifts to GSp(4). https://arxiv.org/abs/1310.2552

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