Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The cocenter-representation duality   Affine Hecke algebras arise naturally in the study of smooth representations
of reductive $p$-adic groups. Finite dimensional complex representations of
affine Hecke algebras (under some restriction on the isogeny class and the
parameter function) has been studied by many mathematicians, including
Kazhdan-Lusztig \cite{KL}, Ginzburg \cite{CG}, Lusztig \cite{L1}, Reeder
\cite{Re}, Opdam-Solleveld \cite{OS}, Kato \cite{Kat}, etc. The approaches are
either geometric or analytic.
  In this note, we'll discuss a different route, via the so-called
"cocenter-representation duality", to study finite dimensional representations
of affine Hecke algebras (for arbitrary isogeny class and for a generic complex
parameter). This route is more algebraic, and allows us to work with complex
parameters, instead of equal parameters or positive parameters. We also expect
that it can be eventually applied to the "modular case" (for representations
over fields of positive characteristic and for parameter equal to a root of
unity).

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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas