The Lusztig automorphism of the \(q\)-Onsager algebra

DOI10.1016/j.jalgebra.2018.03.026zbMath1464.17022arXiv1706.05546OpenAlexW2963229265MaRDI QIDQ1647326

Paul M. Terwilliger

Publication date: 26 June 2018

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.05546

zbMATH Keywords

tridiagonal pair\(q\)-Onsager algebra

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Automorphisms, derivations, other operators for Lie algebras and super algebras (17B40) Quantum equilibrium statistical mechanics (general) (82B10) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items

Hall algebras and quantum symmetric pairs. II: Reflection functors ⋮ Serre-Lusztig relations for \(\imath\) quantum groups ⋮ An infinite-dimensional \(\square_q\)-module obtained from the \(q\)-shuffle algebra for affine \(\mathfrak{sl}_2\) ⋮ Braid group action for the \(q\)-Onsager algebra ⋮ The alternating central extension for the positive part of \(U_q(\hat{\mathfrak{sl}}_2)\) ⋮ Braid group action and quasi-split affine 𝚤quantum groups I ⋮ The compact presentation for the alternating central extension of the \(q\)-Onsager algebra ⋮ Twisting finite-dimensional modules for the \(q\)-Onsager algebra \(\mathcal{O}_q\) via the Lusztig automorphism ⋮ Unnamed Item ⋮ The alternating presentation of \(U_q(\widehat{gl_2})\) from Freidel-Maillet algebras ⋮ The alternating central extension of the \(q\)-Onsager algebra ⋮ An action of the free product \(\mathbb{Z}_2 \star \mathbb{Z}_2 \star \mathbb{Z}_2\) on the \(q\)-Onsager algebra and its current algebra ⋮ Tridiagonal pairs of \(q\)-Racah-type and the \(q\)-tetrahedron algebra ⋮ A note on the algebra Uq(sl2) ⋮ The alternating PBW basis for the positive part of Uq(sl^2) ⋮ Serre-Lusztig relations for \(\imath\) quantum groups. II ⋮ FRT presentation of classical Askey-Wilson algebras ⋮ The alternating central extension of the Onsager Lie algebra

Cites Work

• Unnamed Item
• Unnamed Item
• The universal Askey-Wilson algebra
• Coideal algebras from twisted Manin triples
• Quantum symmetric Kac-Moody pairs
• The \(q\)-Onsager algebra and the positive part of \(U_q(\hat{\mathfrak{sl}}_2)\)
• A classification of sharp tridiagonal pairs
• Braid group actions on coideal subalgebras of quantized enveloping algebras
• The subconstituent algebra of an association scheme. III
• Generalized \(q\)-Onsager algebras and boundary affine Toda field theories
• Tridiagonal pairs of \(q\)-Racah type
• An integrable structure related with tridiagonal algebras
• Deformed Dolan-Grady relations in quantum integrable models
• A new (in)finite-dimensional algebra for quantum integrable models
• The \(q\)-deformed analogue of the Onsager algebra: beyond the Bethe ansatz approach
• A new current algebra and the reflection equation
• The half-infinite XXZ chain in Onsager's approach
• TWO RELATIONS THAT GENERALIZE THE Q-SERRE RELATIONS AND THE DOLAN-GRADY RELATIONS
• The central extension of the reflection equations and an analog of Miki’s formula
• Analogues of Lusztig's higher order relations for the q-Onsager algebra
• THE AUGMENTED TRIDIAGONAL ALGEBRA
• LEONARD PAIRS AND THE ASKEY–WILSON RELATIONS
• A deformed analogue of Onsager’s symmetry in the XXZ open spin chain
• Exact spectrum of the XXZ open spin chain from theq-Onsager algebra representation theory
• A family of tridiagonal pairs and related symmetric functions
• Two linear transformations each tridiagonal with respect to an eigenbasis of the other