Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gauss-Lusztig Decomposition for $GL_q^+(N,R)$ and Representation by
  q-Tori   We found an explicit construction of a representation of the positive quantum
group $GL_q^+(N,\R)$ and its modular double $GL_{q\til[q]}^+(N,\R)$ by positive
essentially self-adjoint operators. Generalizing Lusztig's parametrization, we
found a Gauss type decomposition for the totally positive quantum group
$GL_q^+(N,\R)$ for $|q|=1$, parametrized by the standard decomposition of the
longest element $w_0\in W=S_{N-1}$. Under this parametrization, we found
explicitly the relations between the standard quantum variables, the relations
between the quantum cluster variables, and realizing them using non-compact
generators of the $q$-tori $uv=q^2 vu$ by positive essentially self-adjoint
operators. The modular double arises naturally from the transcendental
relations, and an $L^2(GL_{q\til[q]}^+(N,\R))$ space in the von Neumann setting
can also be defined.

18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
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The categories of this paper are: gr-qc