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Actions of Lie algebra $\mathfrak{sl}_2$ on symmetric polynomials and on Young diagrams

UDC 512.81 We propose two realizations of representations of the complex Lie algebra $\mathfrak{sl}_2$ on the algebra of symmetric polynomials $\Lambda_n$ by differential operators. For each of these realizations, the actions on Schur polynomials are determined and the decomposition of $\Lambda_n$...

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Bibliographic Details
Date:	2026
Main Authors:	Bedratyuk, L., Бедратюк, Леонід
Format:	Article
Language:	Ukrainian
Published:	Institute of Mathematics, NAS of Ukraine 2026
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/8860
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Journal Title:	Ukrains’kyi Matematychnyi Zhurnal
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