Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global Iwasawa-decomposition of SL($n$, $\mathbb{A}_{\mathbb{Q}}$)   We discuss the Iwasawa-decomposition of a general matrix in SL($n$,
$\mathbb{Q}_p$) and SL($n$, $\mathbb{R}$). For SL($n$, $\mathbb{Q}_p$) we
define an algorithm for computing a complete Iwasawa-decomposition and give a
formula parameterizing the full family of decompositions. Furthermore, we prove
that the $p$-adic norms of the coordinates on the Cartan torus are unique
across all decompositions and give a closed formula for them which is proven
using induction. For the case SL($n$, $\mathbb{R}$), the decomposition is
unique and we give formulae for the complete decomposition which are also
proven inductively. Lastly we outline a method for deriving the norms of the
coordinates on the Cartan torus in the framework of representation theory. This
yields a simple formula valid globally which expresses these norms in terms of
the vector norms of generalized Pl\"ucker coordinates.

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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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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: econ
15
The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys