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Characters of Depth-Zero, Supercuspidal Representations of the Rank-2 Symplectic Group
- Source :
- Canadian Journal of Mathematics. 52:306-331
- Publication Year :
- 2000
- Publisher :
- Canadian Mathematical Society, 2000.
-
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.
- Subjects :
- Symplectic group
Rank (linear algebra)
General Mathematics
010102 general mathematics
Symplectic representation
01 natural sciences
Algebra
Character (mathematics)
0103 physical sciences
Lie algebra
010307 mathematical physics
0101 mathematics
Mathematics::Representation Theory
Symplectomorphism
Moment map
Springer correspondence
Mathematics
Subjects
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 52
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi...........77a8e3dfd2120bea9c41459d30ee67e4