Geodesic
Characters of Depth-Zero, Supercuspidal Representations of the Rank-2 Symplectic Group
Canadian journal of mathematics, Tome 52 (2000) no. 2, pp. 306-331

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-2000-014-3
Mots-clés : 22E50, 22E35 
Cunningham, Clifton. Characters of Depth-Zero, Supercuspidal Representations of the Rank-2 Symplectic Group. Canadian journal of mathematics, Tome 52 (2000) no. 2, pp. 306-331. doi: 10.4153/CJM-2000-014-3
@article{10_4153_CJM_2000_014_3,
     author = {Cunningham, Clifton},
     title = {Characters of {Depth-Zero,} {Supercuspidal} {Representations} of the {Rank-2} {Symplectic} {Group}},
     journal = {Canadian journal of mathematics},
     pages = {306--331},
     year = {2000},
     volume = {52},
     number = {2},
     doi = {10.4153/CJM-2000-014-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2000-014-3/}
}
TY  - JOUR
AU  - Cunningham, Clifton
TI  - Characters of Depth-Zero, Supercuspidal Representations of the Rank-2 Symplectic Group
JO  - Canadian journal of mathematics
PY  - 2000
SP  - 306
EP  - 331
VL  - 52
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2000-014-3/
DO  - 10.4153/CJM-2000-014-3
ID  - 10_4153_CJM_2000_014_3
ER  - 
%0 Journal Article
%A Cunningham, Clifton
%T Characters of Depth-Zero, Supercuspidal Representations of the Rank-2 Symplectic Group
%J Canadian journal of mathematics
%D 2000
%P 306-331
%V 52
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2000-014-3/
%R 10.4153/CJM-2000-014-3
%F 10_4153_CJM_2000_014_3

[AD] [AD] Adler, J. and Debacker, S., Moy-Prasad filtrations and harmonic analysis. Draft, 1997. Google Scholar

[Cu] [Cu] Cunningham, C., Some results on elliptic orbital integrals. In preparation. Google Scholar

[K] [K] Kazhdan, D., Proof of Springer's hypothesis. Israel J. Math. 28(1977), 272–286. Google Scholar

[KL] [KL] Kazhdan, D. and Lusztig, G., Fixed point varieties on affine flag manifolds. Israel J. Math. (2) 62(1988), 129–168. Google Scholar

[L1] [L.1] Lusztig, G., Intersection cohomology complexes on a reductive group. Invent.Math. 75(1984), 205–272. Google Scholar

[L2] [L.2] Lusztig, G., Character sheaves I. Adv. Math. 56(1985), 193–297. Google Scholar

Character sheaves II. Adv. Math. 57(1985), 226–265. Google Scholar

Character sheaves III. Adv. Math. 57(1985), 266–315. Google Scholar

Character sheaves IV. Adv. Math. 59(1986), 1–63. Google Scholar

Character sheaves V. Adv. Math. 61(1986), 103–155. Google Scholar

[Mu] [Mu] Murnaghan, F., Characters of supercuspidal representations of classical groups. Ann. Sci. École Norm Sup. (4), (1) 29(1996), 45–105. Google Scholar

[MP] [MP] Moy, A. and Prasad, G., Jacquet functors and unrefined minimal K-types. Comment. Math. Helv. (1) 71(1996), 98–121. Google Scholar

[Sp] [Sp] Spaltenstein, N., Polynomials over local fields, nilpotent orbits and conjugacy classes in Weyl groups. Astérisque 168(1988), 191–217. Google Scholar

[Wa1] [Wa.1] Waldspurger, J.-L., Quelques questions sur les intégrales orbitales unipotentes et les algèbres de Hecke. Bull. Soc. Math. France 124(1996), 1–34. Google Scholar

[Wa2] [Wa.2] Waldspurger, J.-L., Le lemme fondamental implique le transfert. Compositio Math. 105(1997), 153–236. Google Scholar

Cité par Sources :