Spectral Theory of the Nazarov-Sklyanin Lax Operator

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2023
• Main Authors: Mickler, Ryan, Moll, Alexander
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2023
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212021
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Spectral Theory of the Nazarov-Sklyanin Lax Operator. Ryan Mickler and Alexander Moll. SIGMA 19 (2023), 063, 22 pages

In their study of Jack polynomials, Nazarov-Sklyanin introduced a remarkable new graded linear operator 𝓛: 𝐹[𝓌] → 𝐹[𝓌] where 𝐹 is the ring of symmetric functions, and w is a variable. In this paper, we (1) establish a cyclic decomposition 𝐹[𝓌] ≅ ⨁λ 𝑍(𝑗λ, 𝓛) into finite-dimensional 𝓛-cyclic subspaces...