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Some Supercuspidal Representations of Sp4(k)

Published online by Cambridge University Press:  20 November 2018

Charles Asmuth
Charles Asmuth*
Affiliation:
Rutgers University, Newark, New Jersey
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 39 , Issue 1 , 01 February 1987 , pp. 1 - 7
Copyright
Copyright © Canadian Mathematical Society 1987

References

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