The wavefront set: bounds for the Langlands parameter
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208_2025_Article_3278.pdf
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Author(s)
Ciubotaru, Dan
Kim, Ju-Lee
Date Issued
September 9, 2025
Journal
Mathematische Annalen
Publisher
Springer Berlin Heidelberg
Citation
Ciubotaru, D., Kim, JL. The wavefront set: bounds for the Langlands parameter. Math. Ann. 393, 1827–1861 (2025).
Version
Final published version
Abstract
For an irreducible smooth representation of a connected reductive p-adic group, two important associated invariants are the wavefront set and the (partly conjectural) Langlands parameter. While a wavefront set consists of p-adic nilpotent orbits, one constituent of the Langlands parameter is a complex nilpotent orbit in the dual Lie algebra. For unipotent representations in the sense of Lusztig, the corresponding nilpotent orbits on the two sides are related via the Lusztig–Spaltenstein duality (Ciubotaru et al. in Am J Math arXiv:2112.14354v4 , J Reine Angew Math (Crelles J) 823:191–253, 2025). In this paper, we formulate a general upper-bound conjecture and several variants relating the nilpotent orbits that appear in the wavefront set and in the Langlands parameter. We also verify these expectations in some cases, including the depth-zero supercuspidal representations of classical groups and all the irreducible representations of G2.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1007/s00208-025-03278-4
