The Gelfand–Graev representation of GSp(4,𝔽_q)

Abstract

In this article, we demonstrate a technique for calculating the irreducible representations of the endomorphism algebra of the Gelfand–Graev representations of the general symplectic group $\text{GSp}(4,{\mathbb{F}}_q),$ where q is an odd prime power.

Keywords:

• Finite groups
• Gelfand-Graev
• Green functions
• representations

2000 Mathematics Subject Classification.:

• 20C08
• 20C33
• 20G05
• 20G40

Acknowledgements

The authors would like to thank Alex Mueller for explaining how to use zeta functions of curves to compute character sums.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The authors would like to thank Alex Mueller for explaining how to use zeta functions of curves to compute character sums.