# Quasi-polynomials and the Bethe Ansatz

@article{Mukhin2006QuasipolynomialsAT, title={Quasi-polynomials and the Bethe Ansatz}, author={Evgeny Mukhin and Alexander N. Varchenko}, journal={arXiv: Quantum Algebra}, year={2006} }

We study solutions of the Bethe Ansatz equation related to the trigonometric Gaudin model associated to a simple Lie algebra g and a tensor product of irreducible finite-dimensional representations. Having one solution, we describe a construction of new solutions. The collection of all solutions obtained from a given one is called a population. We show that the Weyl group of g acts on the points of a population freely and transitively (under certain conditions).
To a solution of the Bethe…

## 21 Citations

On the Gaudin model of type G2

- Mathematics, PhysicsCommunications in Contemporary Mathematics
- 2019

We derive a number of results related to the Gaudin model associated to the simple Lie algebra of type G2. We compute explicit formulas for solutions of the Bethe ansatz equations associated to the…

Spaces of quasi-exponentials and representations of gln

- Mathematics
- 2008

We consider the action of the Bethe algebra on , the weight subspace of weight of the tensor product of k polynomial irreducible -modules with highest weights , respectively. The Bethe algebra…

On the Gaudin model associated to Lie algebras of classical types

- Mathematics, Physics
- 2015

We derive explicit formulas for solutions of the Bethe Ansatz equations of the Gaudin model associated to the tensor product of one arbitrary finite-dimensional irreducible module and one vector…

XXZ-type Bethe ansatz equations and quasi-polynomials

- Mathematics
- 2012

We study solutions of the Bethe ansatz equation for the XXZ-type integrable model associated with the Lie algebra sl_N. We give a correspondence between solutions of the Bethe ansatz equations and…

XXZ-type Bethe ansatz equations and quasi-polynomials

- Mathematics, Physics
- 2012

We study solutions of the Bethe ansatz equation for the XXZ -type integrable model associated with the Lie algebra slN . We give a correspondence between solutions of the Bethe ansatz equations and…

Populations of solutions to cyclotomic Bethe equations

- Mathematics
- 2015

We study solutions of the Bethe Ansatz equations for the cyclotomic Gaudin model of (Vicedo B., Young C.A.S., arXiv:1409.6937). We give two interpretations of such solutions: as critical points of a…

Dynamical Bethe algebra and functions on pairs of quasi-polynomials

- Physics
- 2021

We consider the space of functions on the Cartan subalgebra of with values in the zero weight subspace of a tensor product of irreducible finite-dimensional -modules. We consider the algebra of…

Bethe Ansatz Equations for Orthosymplectic Lie Superalgebras and Self-dual Superspaces

- Physics, MathematicsAnnales Henri Poincaré
- 2021

We study solutions of the Bethe ansatz equations associated to the orthosymplectic Lie superalgebras osp2m+1|2n and osp2m|2n . Given a solution, we define a reproduction procedure and use it to…

q-hypergeometric solutions of quantum differential equations, quantum Pieri rules, and Gamma theorem

- Mathematics, PhysicsJournal of Geometry and Physics
- 2019

Abstract We describe q -hypergeometric solutions of the equivariant quantum differential equations and the associated qKZ difference equations for the cotangent bundle T ∗ F λ of a partial flag…

Solutions of $\mathfrak{gl}_{m|n}$ XXX Bethe ansatz equation and rational difference operators

- Mathematics, Physics
- 2018

We study solutions of the Bethe ansatz equations of the non-homogeneous periodic XXX model associated to super Yangian $\mathrm Y(\mathfrak{gl}_{m|n})$. To a solution we associate a rational…

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