Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Harmonic and invariant measures on foliated spaces   We consider the family of harmonic measures on a lamination $\mathcal{L}$ of
a compact space $X$ by locally symmetric spaces $L$ of noncompact type, i.e.
$L\simeq \Gamma_L\backslash G/K$. We establish a natural bijection between
these measures and the measures on an associated lamination foliated by
$G$-orbits, $\hat{\mathcal{L}}$ which are right invariant under a minimal
parabolic (Borel) subgroup $B < G$. In the special case when $G$ is split,
these measures correspond to the measures that are invariant under both the
Weyl chamber flow and the stable horospherical flows on a certain bundle over
the associated Weyl chamber lamination. We also show that the measures on
$\hat{\mathcal{L}}$ right invariant under two distinct minimal parabolics, and
therefore all of $G$, are in bijective correspondence with the
holonomy-invariant ones.

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The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
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The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex