2015/01/27 by Banafsheh Farang-Hariri, Farang-Hariri, Banafsheh
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.1501.06793
openalex publication_date 2015/01/27 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
This paper deals with the geometric local theta correspondence at the Iwahori\nlevel for dual reductive pairs of type II over a non Archimedean field F of\ncharacteristic p\≠ 2 in the framework of the geometric Langlands program.\nFirst we construct and study the geometric version of the invariants of the\nWeil representation of the Iwahori-Hecke algebras. In the particular case of\n(GL1, GLm) we give a complete geometric description of the corresponding\ncategory. The second part of the paper deals with geometric local Langlands\nfunctoriality at the Iwahori level in a general setting. Given two reductive\nconnected groups G, H over F and a morphism checkG\×\n\SL2\→ checkH of Langlands dual groups, we construct a bimodule\nover the affine extended Hecke algebras of H and G that should realize the\ngeometric local Arthur-Langlands functoriality at the Iwahori level. Then, we\npropose a conjecture describing the geometric local theta correspondence at the\nIwahori level constructed in the first part in terms of this bimodule and we\nprove our conjecture for pairs (GL1, GLm).\n