Geometric local theta correspondence for dual reductive pairs of type II\n at the Iwahori level

2013/10/25 by Banafaheh Farang-Hariri, Farang-Hariri, Banafaheh
Mathematics · #14D24 #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.1310.6940

openalex publication_date 2013/10/25 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28

Abstract

In this paper we are interested in the geometric local theta correspondence\nat the Iwahori level for dual reductive pairs (G,H) of type II over a\nnon-Archimedean field of characteristic p\≠ 2 in the framework of the\ngeometric Langlands program. We consider the geometric version of the\nI_H\× I_G-invariants of the Weil representation\n\S^I_H\× I_G as a bimodule under the of action\nIwahori-Hecke algebras \H_I_G and \H_I_H and we\ngive some partial geometric description of the corresponding category under the\naction of Hecke functors. We also define geometric Jacquet functors for any\nconnected reductive group G at the Iwahori level and we show that they\ncommute with the Hecke action of the \H_I_L-subelgebra of\n\H_I_G for a Levi subgroup L.\n

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