Ordinary GL₂(F)-representations in characteristic two via affine Deligne-Lusztig constructions

2018/02/07 by Alexander B. Ivanov, Ivanov, Alexander B.
Mathematics · #11F70 #11S37 #14M15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT #msc:11F70 #msc:11S37 #msc:14M15

paper · pdf · doi:10.48550/arxiv.1802.02456

27 pages

arxiv created 2018/02/07 · openalex publication_date 2018/02/07 · arxiv updated 2018/02/08 · openalex created_date 2022/09/04 · openalex updated_date 2026/07/28

Abstract

The group \GL₂ over a local field with (residue) characteristic 2 possesses much more smooth supercuspidal ℓ-adic representations, than over a local field of residue characteristic > 2. One way to construct these representations is via the theory of types of Bushnell-Kutzko. We construct many of them in the cohomology of certain extended affine Deligne-Lusztig varieties attached to \GL₂ and wildly ramified maximal tori in it. Then we compare our construction with the type-theoretic one. The corresponding extended affine Deligne-Lusztig varieties were introduced in a preceding article. Also in the present case they turn out to be zero-dimensional.

Related

• Affine Deligne-Lusztig varieties of higher level and the local Langlands correspondence for GL₂
• Deligne-Lusztig Constructions for Division Algebras and the Local Langlands Correspondence
• The cohomology of the affine Deligne-Lusztig varieties in the affine flag manifold of GL₂
• Decomposition of higher Deligne-Lusztig representations
• Extended Deligne-Lusztig varieties for general and special linear groups