2024/01/14 by Roman Bezrukavnikov, Bezrukavnikov, Roman, Charlotte Chan +1 · 3 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2401.07189
openalex publication_date 2024/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study parabolic induction producing ℓ-adic sheaves on a parahoric subgroup scheme in the loop group of a reductive group. Under a genericity assumption on the input data, we prove that it produces conjugation equivariant perverse sheaves on the parahoric subgroup; this is upgraded to a t-exact equivalence of categories of ℓ-adic sheaves. An iterative version of the construction produces such a perverse sheaf starting from a geometric analogue of the data considered by J.-K. Yu and J. Kim. We prove, under a mild condition on q, that generic parabolic induction from a parahoric torus realizes the character of the representation arising from the associated parahoric Deligne--Lusztig induction, which is known to parametrize the Fintzen--Kaletha--Spice twist of types. In the simplest interesting setting, our construction produces a simple perverse sheaf associated to a sufficiently nontrivial multiplicative local system on a torus, resolving a conjecture of Lusztig.