A new current algebra and the reflection equation

DOI10.1007/S11005-010-0380-XzbMath1187.81166arXiv0906.1482OpenAlexW2066622885MaRDI QIDQ965886

Pascal Baseilhac, Keiichi Shigechi

Publication date: 26 April 2010

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

Full work available at URL: https://arxiv.org/abs/0906.1482

zbMATH Keywords

current algebrareflection equation\(q\)-Onsager algebraquantum integrable models

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Exactly and quasi-solvable systems arising in quantum theory (81U15) Applications of Lie algebras and superalgebras to integrable systems (17B80) Yang-Baxter equations (16T25)

Related Items (37)

Using Catalan words and a \(q\)-shuffle algebra to describe the Beck PBW basis for the positive part of \(U_q( \widehat{\mathfrak{sl}}_2)\) ⋮ The Lusztig automorphism of the \(q\)-Onsager algebra ⋮ Analogues of Lusztig's higher order relations for the q-Onsager algebra ⋮ An infinite-dimensional \(\square_q\)-module obtained from the \(q\)-shuffle algebra for affine \(\mathfrak{sl}_2\) ⋮ A compact presentation for the alternating central extension of the positive part of Uq(sl^2) ⋮ Braid group action for the \(q\)-Onsager algebra ⋮ Theq-Onsager algebra and multivariableq-special functions ⋮ The alternating central extension for the positive part of \(U_q(\hat{\mathfrak{sl}}_2)\) ⋮ Circular bidiagonal pairs ⋮ Using a q-shuffle algebra to describe the basic module V(Λ_0) for the quantized enveloping algebra Uq(sl^2) ⋮ The q-Racah polynomials from scalar products of Bethe states ⋮ 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 ⋮ Tridiagonal pairs, alternating elements, and distance-regular graphs ⋮ Coideal algebras from twisted Manin triples ⋮ The half-infinite XXZ chain in Onsager's approach ⋮ Correlation functions of the half-infinite XXZ spin chain with a triangular boundary ⋮ A conjecture concerning the \(q\)-Onsager algebra ⋮ Form factors of the half-infinite XXZ spin chain with a triangular boundary ⋮ The alternating presentation of \(U_q(\widehat{gl_2})\) from Freidel-Maillet algebras ⋮ The alternating central extension of the \(q\)-Onsager algebra ⋮ Non-abelian symmetries of the half-infinite XXZ spin chain ⋮ The \(q\)-Onsager algebra and the positive part of \(U_q(\hat{\mathfrak{sl}}_2)\) ⋮ The \(q\)-Onsager algebra and the universal Askey-Wilson 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 ⋮ Generalized \(q\)-Onsager algebras and boundary affine Toda field theories ⋮ FRT presentation of the Onsager algebras ⋮ Modified algebraic Bethe ansatz for XXZ chain on the segment. III. Proof ⋮ A Drinfeld type presentation of affine \(\imath\) quantum groups. I: Split ADE type ⋮ The alternating PBW basis for the positive part of Uq(sl^2) ⋮ Higher rank classical analogs of the Askey-Wilson algebra from the sl_N Onsager algebra ⋮ The \(q\)-Onsager algebra and its alternating central extension ⋮ A Drinfeld-type presentation of affine \(\imath\) quantum groups. II: Split BCFG type ⋮ FRT presentation of classical Askey-Wilson algebras ⋮ Circular Hessenberg pairs ⋮ A bispectral q-hypergeometric basis for a class of quantum integrable models ⋮ The alternating central extension of the Onsager Lie algebra

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