A new current algebra and the reflection equation

Abstract

We establish an explicit algebra isomorphism between the quantum reflection algebra for the $U_q(\widehat{s{l}_2})$ R-matrix and a new type of current algebra. These two algebras are shown to be two realizations of a special case of tridiagonal algebras (q-Onsager).

14 pages; v2: More details in Section 4; Typos corrected; References added; To appear in Lett. Math. Phys

References in corpus (2)

• Some algebra related to $P$-and $Q$-polynomial association schemes
• Two relations that generalize the $q$-Serre relations and the Dolan-Grady relations

Cited by in corpus (38)

• The half-infinite XXZ chain in Onsager's approach
• Modified algebraic Bethe ansatz for XXZ chain on the segment - III - Proof
• The Universal Askey-Wilson Algebra
• Set-theoretical reflection equation: Classification of reflection maps
• Correlation functions of the half-infinite XXZ spin chain with a triangular boundary
• Coideal algebras from twisted Manin triples
• The $q$-Onsager Algebra and the Universal Askey-Wilson Algebra
• Non-Abelian symmetries of the half-infinite XXZ spin chain
• The alternating central extension of the $q$-Onsager algebra
• The alternating presentation of $U_q(\widehat{g{l}_2})$ from Freidel-Maillet algebras
• Generalised Onsager Algebra in Quantum Lattice Models
• FRT presentation of classical Askey-Wilson algebras
• Generalized q-Onsager algebras and boundary affine Toda field theories
• A Drinfeld type presentation of affine $ı$quantum groups II: split BCFG type
• FRT presentation of the Onsager algebras
• Generalized q-Onsager Algebras and Dynamical K-matrices
• 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
• The alternating PBW basis for the positive part of $U_q({\widehat{\mathfrak{sl}}}_2)$
• Form factors of the half-infinite XXZ spin chain with a triangular boundary
• The alternating central extension for the positive part of $U_q({\widehat{\mathfrak{sl}}}_2)$
• A conjecture concerning the $q$-Onsager algebra
• The $q$-Onsager algebra and its alternating central extension
• A compact presentation for the alternating central extension of the positive part of $U_q({\widehat{\mathfrak{sl}}}_2)$
• The $q-$Onsager algebra and multivariable $q-$special functions
• Analogues of Lusztig's higher order relations for the q-Onsager algebra
• Central extension of the reflection equations and an analog of Miki's formula
• Using Catalan words and a $q$-shuffle algebra to describe the Beck PBW basis for the positive part of $U_q({\widehat{\mathfrak{sl}}}_2)$
• A bispectral q-hypergeometric basis for a class of quantum integrable models
• The algebra $U_q^{+}$ and its alternating central extension ${\mathcal{U}}_q^{+}$
• Circular Hessenberg Pairs
• Tridiagonal pairs, alternating elements, and distance-regular graphs
• An Infinite-Dimensional ${\square }_q$-Module Obtained from the $q$-Shuffle Algebra for Affine ${\mathfrak{sl}}_2$
• Universal TT- and TQ-relations via centrally extended q-Onsager algebra
• Reflection equation for the N=3 Cremmer-Gervais R-matrix
• Circular bidiagonal pairs
• Parity anomaly from LSM: exact valley symmetries on the lattice
• Using a $q$-shuffle algebra to describe the basic module $V({\Lambda }_0)$ for the quantized enveloping algebra $U_q({\widehat{\mathfrak{sl}}}_2)$
• A new PBW basis for the alternating central extension of the $q$-Onsager algebra