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Characters of Depth-Zero, Supercuspidal Representations of the Rank-2 Symplectic Group

  • Clifton Cunningham (a1)

Abstract

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.

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References

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[AD] Adler, J. and Debacker, S., Moy-Prasad filtrations and harmonic analysis. Draft, 1997.
[Cu] Cunningham, C., Some results on elliptic orbital integrals. In preparation.
[K] Kazhdan, D., Proof of Springer's hypothesis. Israel J. Math. 28(1977), 272286.
[KL] Kazhdan, D. and Lusztig, G., Fixed point varieties on affine flag manifolds. Israel J. Math. (2) 62(1988), 129168.
[L.1] Lusztig, G., Intersection cohomology complexes on a reductive group. Invent.Math. 75(1984), 205272.
[L.2] Lusztig, G., Character sheaves I. Adv. Math. 56(1985), 193297.
Character sheaves II. Adv. Math. 57(1985), 226265.
Character sheaves III. Adv. Math. 57(1985), 266315.
Character sheaves IV. Adv. Math. 59(1986), 163.
Character sheaves V. Adv. Math. 61(1986), 103155.
[Mu] Murnaghan, F., Characters of supercuspidal representations of classical groups. Ann. Sci. École Norm Sup. (4), (1) 29(1996), 45105.
[MP] Moy, A. and Prasad, G., Jacquet functors and unrefined minimal K-types. Comment. Math. Helv. (1) 71(1996), 98121.
[Sp] Spaltenstein, N., Polynomials over local fields, nilpotent orbits and conjugacy classes in Weyl groups. Astérisque 168(1988), 191217.
[Wa.1] Waldspurger, J.-L., Quelques questions sur les intégrales orbitales unipotentes et les algèbres de Hecke. Bull. Soc. Math. France 124(1996), 134.
[Wa.2] Waldspurger, J.-L., Le lemme fondamental implique le transfert. Compositio Math. 105(1997), 153236.
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