Geodesic
Dynamical $\mathfrak{sl}_2$ Bethe algebra and functions on pairs of quasi-polynomials
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 76 (2021) no. 4, pp. 653-684

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We consider the space $\operatorname{Fun}_{\mathfrak{sl}_2}V[0]$ of functions on the Cartan subalgebra of $\mathfrak{sl}_2$ with values in the zero weight subspace $V[0]$ of a tensor product of irreducible finite-dimensional $\mathfrak{sl}_2$-modules. We consider the algebra $\mathcal B$ of commuting differential operators on $\operatorname{Fun}_{\mathfrak{sl}_2}V[0]$, constructed by Rubtsov, Silantyev, and Talalaev in 2009. We describe the relations between the action of $\mathcal B$ on $\operatorname{Fun}_{\mathfrak{sl}_2}V[0]$ and spaces of pairs of quasi-polynomials. Bibliography: 25 titles.
Keywords: commuting differential operators, eigenfunctions, Weyl group invariance, Bethe Ansatz, Wronskian equation
Mots-clés : quasi-polynomials. 
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     author = {A. N. Varchenko and A. M. Slinkin and D. Thompson},
     title = {Dynamical $\mathfrak{sl}_2$ {Bethe} algebra and functions on pairs of quasi-polynomials},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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A. N. Varchenko; A. M. Slinkin; D. Thompson. Dynamical $\mathfrak{sl}_2$ Bethe algebra and functions on pairs of quasi-polynomials. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 76 (2021) no. 4, pp. 653-684. http://geodesic.mathdoc.fr/item/RM_2021_76_4_a2/