A ratio of alternants formula for loop Schur functions
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Publication:2288019
DOI10.4310/JOC.2020.V11.N2.A7zbMATH Open1430.05129arXiv1504.03782OpenAlexW2999521545WikidataQ126356234 ScholiaQ126356234MaRDI QIDQ2288019
Publication date: 16 January 2020
Published in: Journal of Combinatorics (Search for Journal in Brave)
Abstract: Lam and Pylyavskyy introduced loop symmetric functions as a generalization of symmetric functions. They defined loop Schur functions as generating functions over semistandard tableaux with respect to a `colored weight,' and they proved a Jacobi--Trudi-style determinantal formula for these generating functions. We prove that loop Schur functions can be expressed as a ratio of `loop alternants,' extending the analogy with Schur functions. As an application, we give a new proof of the loop version of the Murnaghan--Nakayama rule.
Full work available at URL: https://arxiv.org/abs/1504.03782
Symmetric functions and generalizations (05E05) Combinatorial aspects of representation theory (05E10) Loop groups and related constructions, group-theoretic treatment (22E67)
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