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):  
Bethe Algebra

scholarly journals Quantum cohomology of the cotangent bundle of a flag variety as a Yangian Bethe algebra

2013 ◽  
Vol 74 ◽  
pp. 56-86 ◽  
Author(s):  
V. Gorbounov ◽  
R. Rimányi ◽  
V. Tarasov ◽  
A. Varchenko
Keyword(s):  
Cotangent Bundle ◽  
Quantum Cohomology ◽  
Flag Variety ◽  
Bethe Algebra

Bethe algebra and the algebra of functions on the space of differential operators of order two with polynomial kernel

2008 ◽  
Vol 14 (1) ◽  
pp. 121-144
Author(s):  
E. Mukhin ◽  
V. Tarasov ◽  
A. Varchenko
Keyword(s):  
Differential Operators ◽  
Polynomial Kernel ◽  
Algebra Of Functions ◽  
Bethe Algebra

scholarly journals Bethe Algebra of Gaudin Model, Calogero–Moser Space, and Cherednik Algebra

2012 ◽  
Vol 2014 (5) ◽  
pp. 1174-1204 ◽  
Author(s):  
E. Mukhin ◽  
V. Tarasov ◽  
A. Varchenko
Keyword(s):  
Gaudin Model ◽  
Cherednik Algebra ◽  
Bethe Algebra

scholarly journals ON SEPARATION OF VARIABLES AND COMPLETENESS OF THE BETHE ANSATZ FOR QUANTUM N GAUDIN MODEL

2009 ◽  
Vol 51 (A) ◽  
pp. 137-145 ◽  
Author(s):  
E. MUKHIN ◽  
V. TARASOV ◽  
A. VARCHENKO
Keyword(s):  
Differential Operator ◽  
Bethe Ansatz ◽  
Differential Operators ◽  
Separation Of Variables ◽  
Polynomial Kernel ◽  
Simple Spectrum ◽  
Gaudin Model ◽  
Bethe Algebra ◽  
One To One ◽  
Evaluation Parameters

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.

scholarly journals Cohomology of a flag variety as a Bethe algebra

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

scholarly journals Bethe Algebra of Homogeneous XXX Heisenberg Model has Simple Spectrum

2009 ◽  
Vol 288 (1) ◽  
pp. 1-42 ◽  
Author(s):  
E. Mukhin ◽  
V. Tarasov ◽  
A. Varchenko
Keyword(s):  
Heisenberg Model ◽  
Simple Spectrum ◽  
Bethe Algebra

scholarly journals Gaudin Hamiltonians generate the Bethe algebra of a tensor power of the vector representation of $\mathfrak{gl}_{N}$

2011 ◽  
Vol 22 (3) ◽  
pp. 463-463 ◽  
Author(s):  
E. Mukhin ◽  
V. Tarasov ◽  
A. Varchenko
Keyword(s):  
Vector Representation ◽  
Tensor Power ◽  
Bethe Algebra
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