Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Pieri rule for Demazure characters of the general linear group   The Pieri rule is a nonnegative, multiplicity-free formula for the Schur
function expansion of the product of an arbitrary Schur function with a single
row Schur function. Key polynomials are characters of Demazure modules for the
general linear group that generalize the Schur function basis of symmetric
functions to a basis of the full polynomial ring. We prove a nonsymmetric
generalization of the Pieri rule by giving a cancellation-free,
multiplicity-free formula for the key polynomial expansion of the product of an
arbitrary key polynomial with a single part key polynomial. Our proof is
combinatorial, generalizing the Robinson--Schensted--Knuth insertion algorithm
on tableaux to an insertion algorithm on Kohnert diagrams.

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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph