Branching rules for irreducible depth-zero supercuspidal representations of SL(2,F), when F has residual characteristic 2

2025/09/01 by Zander Karaganis, Karaganis, Zander, Monica Nevins +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2509.01843

Abstract

We give the decomposition into irreducible representations of the restriction to a maximal compact subgroup of any irreducible depth-zero supercuspidal representation of SL(2,F) when F is a local nonarchimedean field of residual characteristic two. We furthermore provide explicit constructions of these irreducible components in terms of nilpotent orbits, proving a representation-theoretic analogue of the local character expansion that holds even in the wild case of characteristic two.

Citations

• Germ expansion for SL(2) in arbitrary characteristics
• Representations of GL_n(D) near the identity
• Local integrability results in harmonic analysis on reductive groups in\n large positive characteristic

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