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Surveys
Dynamical sl2 Bethe algebra and functions on pairs of quasi-polynomials
A. N. Varchenkoabc, A. M. Slinkinad, D. Thompsona a Department of Mathematics, University of North Carolina at Chapel Hill, USA
b Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
c Moscow Center for Fundamental and Applied Mathematics
d National Research University Higher School of Economics
Abstract:
We consider the space Funsl2V[0] of functions on the Cartan subalgebra of sl2 with values in the zero weight subspace V[0] of a tensor product of irreducible finite-dimensional sl2-modules. We consider the algebra B of commuting differential operators on Funsl2V[0], constructed by Rubtsov, Silantyev, and Talalaev in 2009. We describe the relations between the action of B on Funsl2V[0] and spaces of pairs of quasi-polynomials.
Bibliography: 25 titles.
Keywords:
commuting differential operators, eigenfunctions, Weyl group invariance, Bethe Ansatz, Wronskian equation, quasi-polynomials.
Received: 21.04.2021
Citation:
A. N. Varchenko, A. M. Slinkin, D. Thompson, “Dynamical sl2 Bethe algebra and functions on pairs of quasi-polynomials”, Russian Math. Surveys, 76:4 (2021), 653–684
Linking options:
https://www.mathnet.ru/eng/rm10010https://doi.org/10.1070/RM10010 https://www.mathnet.ru/eng/rm/v76/i4/p105
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Abstract page: | 315 | Russian version PDF: | 95 | English version PDF: | 44 | Russian version HTML: | 126 | References: | 39 | First page: | 6 |
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