Bethe Subalgebras in Twisted Yangians

Abstract

We study analogues of the Yangian of the Lie algebra $g{l}_N$ for the other classical Lie algebras $s{o}_N$ and $s{p}_N$. We call them twisted Yangians. They are coideal subalgebras in the Yangian $Y(g{l}_N)$ of $g{l}_N$ and admit homomorphisms onto the universal enveloping algebras $U(s{o}_N)$ and $U(s{p}_N)$ respectively. In every twisted Yangian we construct a family of maximal commutative subalgebras parametrized by the regular semisimple elements of the corresponding classical Lie algebra. The images in $U(s{o}_N)$ and $U(s{p}_N)$ of these subalgebras are also maximal commutative.

26 pages, amstex, misprints corrected

References in corpus (3)

• Quantum symmetric spaces and related q-orthogonal polynomials
• Representations of Yangians with Gelfand-Zetlin Bases
• Yangians and Classical Lie Algebras

Cited by in corpus (31)

• Gaudin models with irregular singularities
• Quantization of the Gaudin System
• Bethe eigenvectors of higher transfer matrices
• Finite-dimensional irreducible representations of twisted Yangians
• On Dunkl angular momenta algebra
• Feigin-Frenkel center in types B, C and D
• Characteristic Classes of SL(N)-Bundles and Quantum Dynamical Elliptic R-Matrices
• The trigonometric Casimir connection of a simple Lie algebra
• Representations of twisted Yangians associated with skew Young diagrams
• Quantisation and nilpotent limits of Mishchenko-Fomenko subalgebras
• Completeness of Wronskian Bethe equations for rational gl(m|n) spin chains
• Argument Shift Method and Gaudin Model
• Quantization of the shift of argument subalgebras in type A
• Manin Matrices, Quantum Elliptic Commutative Families and Characteristic Polynomial of Elliptic Gaudin Model
• Yangians and their applications
• Bethe subalgebras in Yangians and the wonderful compactification
• di-Langlands correspondence and extended observables
• Centralizers of certain quadratic elements in Poisson--Lie algebras and Argument Shift method
• The $SU(3)\supset SO(3)$ missing label problem and the analytical Bethe ansatz
• Reflection equation and twisted Yangians
• Representations of Yangians associated with skew Young diagrams
• On Bethe eigenvectors and higher transfer matrices for supersymmetric spin chains
• Spectra of Bethe subalgebras of $Y({\mathfrak{gl}}_n)$ in tame representations
• Yangian deformations of $\mathcal{S}$-commutative quantum vertex algebras and Bethe subalgebras
• Resolution of the GL(3) - O(3) state labelling problem via O(3)-invariant Bethe subalgebra of the twisted Yangian
• Quantizing Mishchenko-Fomenko subalgebras for centralizers via affine W-algebras
• Capelli Identities for Classical Lie Algebras
• Symmetric functions for the generating matrix of Yangian of gl_n(C)
• Simplicity of spectra for Bethe subalgebras in $Y({\mathfrak{gl}}_2)$
• On the quantum argument shift method
• Degeneration of Bethe subalgebras in the Yangian of ${\mathfrak{gl}}_n$