Some Supercuspidal Representations of <i>Sp</i><sub>4</sub>(k)
Abstrak
The purpose of this paper is to produce explicit realizations of supercuspidal representations of Sp4(k) where k is a p-adic field with odd residual characteristic. These representations will be constructed using the Weil representation of Sp4(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 SL2(k) associated to 2-dimensional orthogonal groups were used by Casselman [4] and Shalika [9] to produce all supercuspidals of SL2(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.
Penulis (1)
Charles Asmuth
Akses Cepat
- Tahun Terbit
- 1987
- Bahasa
- en
- Sumber Database
- CrossRef
- DOI
- 10.4153/cjm-1987-001-9
- Akses
- Open Access ✓