Local characters of mod-ℓ representations of a p-adic reductive group

2025/10/23 by Cheng-Chiang Tsai, Tsai, Cheng-Chiang · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2510.20509

Abstract

We define the ``lifted character'' of mod-ℓ representations of p-adic reductive groups where ℓ\not=p, on compact elements with pro-orders not divisible by ℓ. We generalize the local character expansion results of Howe, Harish-Chandra and DeBacker to such lifted characters. We show that the result of Moeglin-Waldspurger and Varma on degenerate Whittaker models is valid for the character expansion.

Citations

• Local character expansion for mod-ℓ representations
• Representations of GL_n(D) near the identity
• Explicit asymptotic expansions in p-adic harmonic analysis II
• A twisted Yu construction, Harish-Chandra characters, and endoscopy
• Regular supercuspidal representations
• Nilpotent orbits over ground fields of good characteristic

Cited by

• Local character expansion for mod-ℓ representations

Related

• Local character expansion for mod-ℓ representations
• Characters of locally analytic representations of p-adic reductive groups
• Local Summability of Characters on p-adic Reductive Groups
• Modular representations of p-adic groups
• Questions on mod p representations of reductive p-adic groups