This paper expresses the character of certain depth-zero supercuspidal representations of the rank-2 symplectic group as the Fourier transform of a finite linear combination of regular elliptic orbital integrals---an expression which is ideally suited for the study of the stability of those characters. Building on work of F.~Murnaghan, our proof involves Lusztig's Generalised Springer Correspondence in a fundamental way, and also makes use of some results on elliptic orbital integrals proved elsewhere by the author using Moy-Prasad filtrations of $p$-adic Lie algebras. Two applications of the main result are considered toward the end of the paper.

MSC Classifications:

22E50, 22E35 show english descriptions Representations of Lie and linear algebraic groups over local fields [See also 20G05]
Analysis on $p$-adic Lie groups 22E50 - Representations of Lie and linear algebraic groups over local fields [See also 20G05]
22E35 - Analysis on $p$-adic Lie groups

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