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

2013/10/09 by Mirko Rösner, Rösner, Mirko
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1310.2552

openalex publication_date 2013/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the Saito-Kurokawa lifting

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