Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Langlands parameters, functoriality and Hecke algebras   Let $G$ and $\tilde G$ be reductive groups over a local field $F$. Let $\eta
: \tilde G \to G$ be a $F$-homomorphism with commutative kernel and commutative
cokernel. We investigate the pullbacks of irreducible admissible
$G$-representations $\pi$ along $\eta$. Following Borel, Adler--Korman and Xu,
we pose a conjecture on the decomposition of the pullback $\eta^* \pi$. It is
formulated in terms of enhanced Langlands parameters and includes
multiplicities. This can be regarded as a functoriality property of the local
Langlands correspondence. We prove this conjecture for three classes: principal
series representation of split groups (over non-archimedean local fields),
unipotent representations (also with $F$ non-archimedean) and inner twists of
$GL_n, SL_n, PGL_n$. Our main techniques involve Hecke algebras associated to
Langlands parameters. We also prove a version of the pullback/functoriality
conjecture for those.

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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg