Dynamical \fraksl₂ Bethe algebra and functions on pairs of quasi-polynomials

2020/07/18 by Alexey Slinkin, Daniel Thompson, Slinkin, A. +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2007.09504

openalex publication_date 2020/07/18 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We consider the space Fun_\fraksl₂V[0] of functions on the Cartan subalgebra of \fraksl₂ with values in the zero weight subspace V[0] of a tensor product of irreducible finite-dimensional \fraksl₂-modules. We consider the algebra \mathcal B of commuting differential operators on Fun_\fraksl₂ V[0], constructed by V.Rubtsov, A.Silantyev, D.Talalaev in 2009. We describe the relations between the action of \mathcal B on Fun_\fraksl₂V[0] and spaces of pairs of quasi-polynomials.

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