The Ramanujan Journal

, Volume 36, Issue 3, pp 305–354 | Cite as

Irreducible characters of \(\mathrm{GSp}(4, q)\) and dimensions of spaces of fixed vectors



In this paper, we compute the conjugacy classes and the list of irreducible characters of \(\mathrm{GSp}(4,q)\), where \(q\) is odd. We also determine precisely which irreducible characters are non-cuspidal and which are generic. These characters are then used to compute dimensions of certain subspaces of fixed vectors of smooth admissible non-supercuspidal representations of \(\mathrm{GSp}(4,F)\), where \(F\) is a non-archimedean local field of characteristic zero with residue field of order \(q\).


Representation theory Finite groups \(p\)-adic groups 

Mathematics Subject Classification

11F46 11F70 11F85 


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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Fordham UniversityBronxUSA

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