Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Branching Indices of Affine A-D-E Diagrams : A Geometrical
  Characterization by Kleinian Singularities   The exceptional configuration of the minimal resolution $\hat{S}_G $ of a
Kleinian quotient surface $S_G (:= \CZ^2/G)$ is depicted by a $A$-$D$-$E$
Coxeter-Dynkin diagram. In this article, we show that branching indices of the
affine $A$-$D$-$E$ diagram is geometrically characterized by a certain special
function $F$ of $S_G$ as the multiplicities of its divisor components in
$\hat{S}_G$, a version parallel to the elliptic fibration near certain types of
simple singular fibers in Kodaira's elliptic surface theory. We further obtain
the uniqueness property of the function $F$ (modular local units) among all
local functions in $S_G$ near the singular point whose divisors in $\hat{S}_G $
display the affine $A$-$D$-$E$ diagram configuration.

23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin