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

  • Jeffery BreedingII


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 



The author would like to thank Ralf Schmidt and Alan Roche for their valuable notes and comments on this paper. The author would especially like to thank the referee for the detailed comments and careful reading of this paper.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Fordham UniversityBronxUSA

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