Formal degree of principal series of quasi-split groups

2026/04/30 by Giulio Ricci
#math.RT

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Abstract

Let G be a quasi-split connected reductive group over a non-archimedean local field F. In this paper, we prove the formal degree conjecture for discrete series representations contained in a principal series of G(F). We first construct a type for each Bernstein component attached to a principal series representation of G(F). We then use these types and the local Langlands correspondence for principal series representations defined in [Sol25] to verify the formal degree conjecture. Our approach follows a similar strategy to [Ric25], reducing the problem to the case of unipotent representations of some other quasi-split group.

Citations

• The Hiraga-Ichino-Ikeda Conjecture for Principal Series of Split p-adic Groups
• On depth-zero characters of p-adic groups
• Affine Hecke algebras for Langlands parameters
• Spectral correspondences for affine Hecke algebras
• Semisimple types for p-adic classical groups
• On the spectral decomposition of affine Hecke algebras

Related

• The Hiraga-Ichino-Ikeda Conjecture for Principal Series of Split p-adic Groups
• Principal series representations of metaplectic groups over local fields
• Reducible principal series representations, and Langlands parameters for\n real groups
• On generic representations of quasi-split reductive groups over local fields of positive characteristic
• Formal Degrees and Parabolic Induction: the Maximal Generic Case