2021/04/27 by Roman Bezrukavnikov, Bezrukavnikov, Roman, Yakov Varshavsky +1 · 1 citation
Mathematics · #22E50 #22E57 #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.2104.13123
openalex publication_date 2021/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a connected reductive group over a field F=\mathbbFq((t)) splitting over \mathbbFq((t)). Following [KV,DR], a tamely unramified Langlands parameter λ:WF→L G(ℚℓ) in general position gives rise to a finite set Πλ of irreducible admissible representations of G(F), called the L-packet. The main goal of this work is to provide a geometric description of characters χπ of π∈Πλ and of their endoscopic linear combinations χλκ in terms of homology of affine Springer fibers, thus establishing an analog of Lusztig conjectures in this case. Furthermore, each χλκ can be described as the trace of Frobenius function of a conjugation equivariant perverse sheaf on the loop group by the sheaf-function correspondence. As another application, we prove that the sum χλst:=∑π∈Πλχπ is stable and show that the χλst's are compatible with inner twistings. More generally, we prove that each χλκ is Eλ,κ-stable.