Дiї алгебри Лi $\mathfrak{sl}_2$ на симетричних многочленах і на дiаграмах Юнга
Abstract
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 $\Lambda_n$ into irreducible representations is obtained. By using the $\mathfrak{sl}_2$-isomorphism between $\Lambda_n$ and the vector space of Young diagrams $\mathbb{Q}\mathcal{Y}_n$ with at most $n$ rows, these representations are transferred to $\mathbb{Q}\mathcal{Y}_n.$
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Advanced Algebra and Geometry
Algebraic structures and combinatorial models
Publication details
- Journal / source
- Ukrains’kyi Matematychnyi Zhurnal
- Volume
- 78
- Issue
- 1-2
- Pages
- 3–21
- Publication date
- 27 January 2026
- Language
- UK