Geodesic
Some Supercuspidal Representations of Sp 4(k)
Canadian journal of mathematics, Tome 39 (1987) no. 1, pp. 1-7

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The purpose of this paper is to produce explicit realizations of supercuspidal representations of Sp 4(k) where k is a p-adic field with odd residual characteristic. These representations will be constructed using the Weil representation of Sp 4(k) associated with a certain 4-dimensional compact orthogonal group OQ over k. The main problem addressed in this paper is the analysis of this representation; we need to find how the supercuspidal summands decompose into irreducible pieces.The problem of decomposing Weil representations has been studied quite a bit already. The Weil representations of SL 2(k) associated to 2-dimensional orthogonal groups were used by Casselman [4] and Shalika [9] to produce all supercuspidals of SL 2(k). The explicit formulas for these representations were used by Sally and Shalika ([10]) to compute the characters and finally to write down a Plancherel formula for that group. 
Asmuth, Charles. Some Supercuspidal Representations of Sp 4(k). Canadian journal of mathematics, Tome 39 (1987) no. 1, pp. 1-7. doi: 10.4153/CJM-1987-001-9
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