Spectra of Bethe subalgebras of \(Y(\mathfrak{gl}_n)\) in tame representations

DOI10.1007/s11005-022-01589-0OpenAlexW3198451457MaRDI QIDQ2089898

Leonid Rybnikov, Inna Mashanova-Golikova, Aleksei Ilin

Publication date: 24 October 2022

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2109.03170

zbMATH Keywords

representation theoryYangiansquantum integrable systemsKirillov-Reshetikhin modulesBethe subalgebras

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Applications of Lie algebras and superalgebras to integrable systems (17B80) Universal enveloping algebras of Lie algebras (16S30)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Spaces of quasi-exponentials and representations of the Yangian \(Y(\mathfrak{gl}_N)\)
• Opers with irregular singularity and spectra of the shift of argument subalgebra
• Simplicity of spectra for Bethe subalgebras in \(\mathrm{Y}(\mathfrak{gl}_2)\)
• Bethe algebra of homogeneous \(XXX\) Heisenberg model has simple spectrum
• The argument shift method and the Gaudin model
• Quantization of the shift of argument subalgebras in type \(A\)
• The Yangians, Bethe Ansatz and combinatorics
• Solutions to the \(XXX\) type Bethe ansatz equations and flag varieties
• Projective wonderful models for toric arrangements
• Degeneration of Bethe subalgebras in the Yangian of \(\mathfrak {gl}_n\)
• On limits of Mishchenko-Fomenko subalgebras in Poisson algebras of semisimple Lie algebras
• Bethe subalgebras in twisted Yangians
• The \(R\)-matrix presentation for the Yangian of a simple Lie algebra
• Bethe subalgebras in Yangians and the wonderful compactification
• On classical limits of Bethe subalgebras in Yangians
• The maximality of certain commutative subalgebras in Yangians
• The Berenstein-Kirillov group and cactus groups
• Crystals and monodromy of Bethe vectors
• Generating operator of \(XXX\) or Gaudin transfer matrices has quasi-exponential kernel
• Crystals and coboundary categories
• Gaudin models with irregular singularities
• Gaudin subalgebras and stable rational curves
• Chow quotients of Grassmannian I
• Representations of Yangians with GelfandZetlin bases
• The maximality of certain commutative subalgebras in the Poisson algebra of a semisimple Lie algebra
• Completeness of the Bethe Ansatz for the Periodic Isotropic Heisenberg Model
• Cactus Group and Monodromy of Bethe Vectors
• Uniqueness of liftings of maximal commutative subalgebras of the Poisson-Lie algebra to the enveloping algebra
• Quantum groups and quantum cohomology
• A Proof of the Gaudin Bethe Ansatz Conjecture
• Quiver varieties and Yangians
• New moduli spaces of pointed curves and pencils of flat connections.

This page was built for publication: Spectra of Bethe subalgebras of \(Y(\mathfrak{gl}_n)\) in tame representations