Dynamical [IMG align=ABSMIDDLE alt=$ \mathfrak{sl}_2$]tex_rm_5278_img1[/IMG] Bethe algebra and functions on pairs of quasi-polynomials

2021 ◽  
Vol 76 (4) ◽  
Author(s):  
Aleksandr Nikolaevich Varchenko ◽  
Alexei Alexandrovich Slinkin ◽  
Daniel Thompson
Keyword(s):  

2013 ◽  
Vol 74 ◽  
pp. 56-86 ◽  
Author(s):  
V. Gorbounov ◽  
R. Rimányi ◽  
V. Tarasov ◽  
A. Varchenko




2012 ◽  
Vol 2014 (5) ◽  
pp. 1174-1204 ◽  
Author(s):  
E. Mukhin ◽  
V. Tarasov ◽  
A. Varchenko


2009 ◽  
Vol 51 (A) ◽  
pp. 137-145 ◽  
Author(s):  
E. MUKHIN ◽  
V. TARASOV ◽  
A. VARCHENKO

AbstractIn this paper, we discuss implications of the results obtained in [5]. It was shown there that eigenvectors of the Bethe algebra of the quantum N Gaudin model are in a one-to-one correspondence with Fuchsian differential operators with polynomial kernel. Here, we interpret this fact as a separation of variables in the N Gaudin model. Having a Fuchsian differential operator with polynomial kernel, we construct the corresponding eigenvector of the Bethe algebra. It was shown in [5] that the Bethe algebra has simple spectrum if the evaluation parameters of the Gaudin model are generic. In that case, our Bethe ansatz construction produces an eigenbasis of the Bethe algebra.



2011 ◽  
Vol 45 (4) ◽  
pp. 252-264 ◽  
Author(s):  
R. Rimányi ◽  
V. Schechtman ◽  
V. Tarasov ◽  
A. Varchenko
Keyword(s):  


2009 ◽  
Vol 288 (1) ◽  
pp. 1-42 ◽  
Author(s):  
E. Mukhin ◽  
V. Tarasov ◽  
A. Varchenko




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