Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric tamely ramified local theta correspondence in the framework of
  the geometric Langlands program   This paper deals with the geometric local theta correspondence at the Iwahori
level for dual reductive pairs of type II over a non Archimedean field $F$ of
characteristic $p\neq 2$ in the framework of the geometric Langlands program.
First we construct and study the geometric version of the invariants of the
Weil representation of the Iwahori-Hecke algebras. In the particular case of
$(GL_1, GL_m)$ we give a complete geometric description of the corresponding
category. The second part of the paper deals with geometric local Langlands
functoriality at the Iwahori level in a general setting. Given two reductive
connected groups $G$, $H$ over $F$ and a morphism $\check{G}\times
\mathrm{SL}_2\to\check{H}$ of Langlands dual groups, we construct a bimodule
over the affine extended Hecke algebras of $H$ and $G$ that should realize the
geometric local Arthur-Langlands functoriality at the Iwahori level. Then, we
propose a conjecture describing the geometric local theta correspondence at the
Iwahori level constructed in the first part in terms of this bimodule and we
prove our conjecture for pairs $(GL_1, GL_m)$.

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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga