Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the fully commutative elements of type $\tilde C$ and faithfulness of
  related towers   We define a tower of injections of $\tilde{C}$-type Coxeter groups $W(\tilde
C_{n})$ for $n\geq 1$. We define a tower of Hecke algebras and we use the
faithfulness at the Coxeter level to show that this last tower is a tower of
injections. Let $W^c(\tilde C_{n})$ be the set of fully commutative elements in
$W(\tilde C_{n})$, we classify the elements of $W^c(\tilde C_{n})$ and give a
normal form for them. We use this normal form to define two injections from
$W^c(\tilde C_{n-1})$ into $W^c(\tilde C_{n})$. We then define the tower of
affine Temperley-Lieb algebras of type $\tilde{C }$ and use the injections
above to prove the faithfulness of this tower.

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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn