Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The shift orbits of the graded Kronecker modules   The Kronecker modules (or matrix pencils) are the representations of the
n-Kronecker quiver K(n) (the quiver with two vertices, namely a sink and a
source, and n arrows) over some fixed field. The universal cover of K(n) is the
n-regular tree with bipartite orientation.
  The paper deals with the representations of the n-regular tree with bipartite
orientation (thus with graded Kronecker modules). The simultaneous
Bernstein-Gelfand-Ponomarev reflection at all sinks will be called the shift
functor, and we consider the orbits under this shift functor. Whereas the
length of a regular module growths exponentially when we apply the shift
functor repeatedly, the radius of such a module growths just linearly.
  To any regular shift orbit, we attach a positive integer r (the minimal
radius of the sink modules in the orbit) and the path in T(n) which starts at
the center p of the sink modules in the orbit and ends at the center q of the
source modules in the orbit. If r is even, then p has to be a sink, otherwise a
source. We call this path the center path of the orbit (since the center of any
module in the orbit lies on this path). If the center path of a shift orbit has
length b, then the orbit contains precisely b flow modules, the remaining
modules are sink modules and source modules. We use this division in order to
index the regular graded Kronecker modules in a coherent way. Conversely, we
show that given a positive integer r and a path in T(n) (starting at a sink iff
r is even), there are regular shift orbits with these invariants.

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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci