Twisted Yangians for symmetric pairs of types B, C, D

Abstract

We study a class of quantized enveloping algebras, called twisted Yangians, associated with the symmetric pairs of types B, C, D in Cartan's classification. These algebras can be regarded as coideal subalgebras of the extended Yangian for orthogonal or symplectic Lie algebras. They can also be presented as quotients of a reflection algebra by additional symmetry relations. We prove an analogue of the Poincare-Birkoff-Witt Theorem, determine their centres and study also extended reflection algebras.

28 pages, final version. Accepted to Math. Z

References in corpus (1)

• From Twisted Quantum Loop Algebras to Twisted Yangians

Cited by in corpus (16)

• Spin Chain Overlaps and the Twisted Yangian
• Isomorphism between the $R$-matrix and Drinfeld presentations of Yangian in types $B$, $C$ and $D$
• The $R$-matrix presentation for the Yangian of a simple Lie algebra
• Representations of twisted Yangians of types B, C, D: I
• Gauge Theory and Boundary Integrability
• Rational Lax matrices from antidominantly shifted extended Yangians: BCD types
• Representations of twisted Yangians of types B, C, D: II
• Twisted Yangians of small rank
• More on Affine Dynkin Quiver Yangians
• Nested algebraic Bethe ansatz for orthogonal and symplectic open spin chains
• Nested algebraic Bethe ansatz for open spin chains with even twisted Yangian symmetry
• On the classification of rational K-matrices
• Isomorphism between twisted $q$-Yangians and affine $ı$quantum groups: type AI
• Affine $ı$quantum groups and twisted Yangians in Drinfeld presentations
• A Drinfeld type presentation of twisted Yangians
• Twisted super Yangians of type AIII and their representations