GKLO representations of twisted Yangians in type AI and quantizations of symmetric quotients of the affine Grassmannian

2025/10/14 by Robin Bartlett, Bartlett, Robin, Tomasz Przeździecki +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2510.12706

openalex publication_date 2025/10/14 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28

Abstract

We construct an analogue of Gerasimov-Kharchev-Lebedev-Oblezin (GKLO) representations for twisted Yangians of type AI, using the recently found current presentation of these algebras due to Lu, Wang and Zhang. These new representations allow us to define interesting truncations of twisted Yangians, which, in the spirit of Ciccoli-Drinfeld-Gavarini quantum duality, reflect the Poisson geometry of homogeneous spaces. As our main result, we prove that a truncated twisted Yangian quantizes a scheme supported on quotients of transverse slices in the affine Grassmannian.

Citations

• Shifted twisted Yangians and affine Grassmannian islices
• Shifted twisted Yangians and finite W-algebras of classical type
• Boundary q-characters of evaluation modules for split quantum affine symmetric pairs
• Shifted twisted Yangians and Slodowy slices in classical Lie algebras
• Singularities of orbit closures in loop spaces of symmetric varieties
• A Drinfeld type presentation of twisted Yangians
• One dimensional representations of finite W-algebras, Dirac reduction and the orbit method
• Reducedness of affine Grassmannian slices in type A
• Comultiplication for shifted Yangians and quantum open Toda lattice
• Twisted loop groups and their affine flag varieties
• Matsuki correspondence for the affine Grassmannian

Cited by

• Minimalistic Presentation and Coideal Structure of Twisted Yangians

Related

• Shifted twisted Yangians and finite W-algebras of classical type
• A Drinfeld type presentation of twisted Yangians
• Twisted Yangians of small rank
• Hamiltonian reduction for affine Grassmannian slices and truncated shifted Yangians
• Shifted twisted Yangians and affine Grassmannian islices