Actions of Lie algebra sl_2 on symmetric polynomials and on Young diagrams - Bedratyuk, L. (Ukrains’kyi Matematychnyi Zhurnal, 2026)
UDC 512.81 We propose two realizations of representations of the complex Lie algebra sl_2 on the algebra of symmetric polynomials Λ_n by differential operators. For each of these realizations, the actions on Schur polynomials are determined and the decomposition of Λ_n into irreducible representations is obtained. By using the sl_2-isomorphism between Λ_n and the vector space of Young diagrams QY_n with at most n rows, these representations are transferred to QY_n.