Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orthogonal Polynomials appearing in SIE grid representations   We show in this article how orthogonal polynomials appear in certain
representations of grid shaped quivers. After a short introduction into the
general notion of quivers and their representations by linear operators we
define the notion of an SIE quiver representation: All intrinsic endomorphisms
arising from circuits in the quiver act as scalar multipliers. We then present
several lemmas that ensure this SIE property of a quiver representation. Ladder
commutator conditions and certain diagram commutativity "up to scalar
multiples" play a central role. The theory will then be applied to three
examples. Extensive calculations shows how Associated Laguerre,
Legendre--Gegenbauer polynomials and binomial distributions fit into the
framework of grid shaped SIE quivers. One can see, that this algebraic point of
view is foundational for orthogonal polynomials and special functions.

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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat