Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Prehomogeneous vector spaces and ergodic theory III   Let H_1=SL(5), H_2=SL(3), H=H_1 \times H_2. It is known that (G,V) is a
prehomogeneous vector space (see [22], [26], [25], for the definition of
prehomogeneous vector spaces). A non-constant polynomial \delta(x) on V is
called a relative invariant polynomial if there exists a character \chi such
that \delta(gx)=\chi(g)\delta(x). Such \delta(x) exists for our case and is
essentially unique. So we define V^{ss}={x in V such that \delta(x) is not
equal to 0}. For x in V_R^{ss}, let H_{x R+}^0 be the connected component of 1
in classical topology of the stabilizer H_{x R}. We will prove that if x in
V_R^ss is "sufficiently irrational", H_{x R+}^0 H_Z is dense in H_R.

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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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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: hep-lat