Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hall polynomials via automorphisms of short exact sequences   We present a sum-product formula for the classical Hall polynomial which is
based on tableaux that have been introduced by T. Klein in 1969. In the
formula, each summand corresponds to a Klein tableau, while the product is
taken over the cardinalities of automorphism groups of short exact sequences
which are derived from the tableau. For each such sequence, one can read off
from the tableau the summands in an indecomposable decomposition, and the size
of their homomorphism and automorphism groups. Klein tableaux are refinements
of Littlewood-Richardson tableaux in the sense that each entry $\ell \geq 2$
carries a subscript $r$. We describe module theoretic and categorical
properties shared by short exact sequences which have the same symbol $\ell_r$
in a given row in their Klein tableau. Moreover, we determine the interval in
the Auslander-Reiten quiver in which indecomposable sequences of $p^n$-bounded
groups which carry such a symbol occur.

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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio