Publications (30)
Universal TT- and TQ-relations via centrally extended q-Onsager algebra
Pascal Baseilhac, Azat M. Gainutdinov, Guillaume Lemarthe
Let be the alternating central extension of the q-Onsager algebra, a comodule algebra over the quantum loop algebra of . We classify one-dimensional representations of…
An integrable structure related with tridiagonal algebras
Pascal Baseilhac
The standard generators of tridiagonal algebras, recently introduced by Terwilliger, are shown to generate a new (in)finite family of mutually commuting operators which extends the…
Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz
Pascal Baseilhac, Rodrigo A. Pimenta
An operator of Heun-Askey-Wilson type is diagonalized within the framework of the algebraic Bethe ansatz using the theory of Leonard pairs. For different specializations and the ge…
A family of tridiagonal pairs and related symmetric functions
Pascal Baseilhac
A family of tridiagonal pairs which appear in the context of quantum integrable systems is studied in details. The corresponding eigenvalue sequences, eigenspaces and the block tri…
Correlation functions of the half-infinite XXZ spin chain with a triangular boundary
Pascal Baseilhac, Takeo Kojima
The half-infinite XXZ spin chain with a triangular boundary is considered in the massive regime. Two integral representations of correlation functions are proposed using bosonizati…
Deformed Dolan-Grady relations in quantum integrable models
Pascal Baseilhac
A new hidden symmetry is exhibited in the reflection equation and related quantum integrable models. It is generated by a dual pair of operators $\{\textsf{A}, \textsf{A}^*\}\in{\c…
Braid group action and root vectors for the -Onsager algebra
Pascal Baseilhac, Stefan Kolb
We define two algebra automorphisms and of the -Onsager algebra , which provide an analog of G. Lusztig's braid group action for quantum groups. These automorph…
FRT presentation of classical Askey-Wilson algebras
Pascal Baseilhac, Nicolas Crampe
Automorphisms of the infinite dimensional Onsager algebra are introduced. Certain quotients of the Onsager algebra are formulated using a polynomial in these automorphisms. In the…
An embedding of the Bannai-Ito algebra in and polynomials
Pascal Baseilhac, Vincent X. Genest, Luc Vinet +1
An embedding of the Bannai-Ito algebra in the universal enveloping algebra of is provided. A connection with the characterization of the little Jacobi po…
Freidel-Maillet type presentations of
Pascal Baseilhac
A unified framework for the Chevalley and equitable presentation of is introduced. It is given in terms of a system of Freidel-Maillet type equations satisfied by a pai…
The q-deformed analogue of the Onsager algebra: Beyond the Bethe ansatz approach
Pascal Baseilhac
The spectral properties of operators formed from generators of the q-Onsager non-Abelian infinite dimensional algebra are investigated. Using a suitable functional representation,…
The -Racah polynomials from scalar products of Bethe states
Pascal Baseilhac, Rodrigo A. Pimenta
The -Racah polynomials are expressed in terms of certain ratios of scalar products of Bethe states associated with Bethe equations of either homogeneous or inhomogeneous type. T…
The q-Heun operator of big q-Jacobi type and the q-Heun algebra
Pascal Baseilhac, Luc Vinet, Alexei Zhedanov
The q-Heun operator of the big q-Jacobi type on the exponential grid is defined. This operator is the most general second order q-difference operator that maps polynomials of degre…
Little and Big Jacobi Polynomials and the Askey-Wilson algebra
Pascal Baseilhac, Xavier Martin, Luc Vinet +1
The little and big q-Jacobi polynomials are shown to arise as basis vectors for representations of the Askey-Wilson algebra. The operators that these polynomials respectively diago…
Fused K-operators and the -Onsager algebra
Guillaume Lemarthe, Pascal Baseilhac, Azat M. Gainutdinov
We study universal solutions to reflection equations with a spectral parameter, so-called K-operators, within a general framework of universal K-matrices - an extended version of t…
An attractive basis for the Onsager algebra
Pascal Baseilhac, Samuel Belliard
Let be the fundamental generators of the Onsager algebra. A linear basis for the Onsager algebra is known as the `zig-zag' basis [IT09]. In this l…
On the second realization for the positive part of of equitable type
Pascal Baseilhac
The equitable presentation of the quantum algebra is considered. This presentation was originally introduced by T. Ito and P. Terwilliger. In this paper, foll…
A bispectral q-hypergeometric basis for a class of quantum integrable models
Pascal Baseilhac, Xavier Martin
For the class of quantum integrable models generated from the Onsager algebra, a basis of bispectral multivariable orthogonal polynomials is exhibited. In a first part, it…
The -Racah polynomials from scalar products of Bethe states II
Pascal Baseilhac, Rodrigo A. Pimenta
The theory of Leonard triples is applied to the derivation of normalized scalar products of on-shell and off-shell Bethe states generated from a Leonard pair. The scalar products t…
FRT presentation of the Onsager algebras
Pascal Baseilhac, Samuel Belliard, Nicolas Crampe
A presentation à la Faddeev-Reshetikhin-Takhtajan (FRT) of the Onsager, augmented Onsager and sl(2)-invariant Onsager algebras is given, using the framework of the non-standard cla…
Higher rank classical analogs of the Askey-Wilson algebra from the Onsager algebra
Pascal Baseilhac, Nicolas Crampe, Rodrigo A. Pimenta
The -Onsager algebra has been introduced by Uglov and Ivanov in 1995. In this letter, a FRT presentation of the -Onsager algebra is given, its current algebra and commu…
The algebra , Onsager algebras and coideal subalgebras: two open problems
Pascal Baseilhac
A brief and elementary introduction to the subject is presented. Two open problems are given.
The Onsager algebra and multivariable special functions
Pascal Baseilhac, Luc Vinet, Alexei Zhedanov
Two sets of mutually commuting difference operators and , such that and generate a homomorphic image of the Onsager algebra for each $…
Asymptotic representations of augmented q-Onsager algebra and boundary K-operators related to Baxter Q-operators
Pascal Baseilhac, Zengo Tsuboi
We consider intertwining relations of the augmented -Onsager algebra introduced by Ito and Terwilliger, and obtain generic (diagonal) boundary -operators in terms of the Cart…
The Heun-Askey-Wilson algebra and the Heun operator of Askey-Wilson type
Pascal Baseilhac, Satoshi Tsujimoto, Luc Vinet +1
The Heun-Askey-Wilson algebra is introduced through generators $\{\boX,\boW\}$ and relations. These relations can be understood as an extension of the usual Askey-Wilson ones. A ce…
The quantum loop algebra of and -Racah type bivariate functions
Pascal Baseilhac, Nicolas Crampe
A unified algebraic framework for two different six-parameter families of bivariate -Racah type functions is given using the representation theory of the quantum loop algebra $\…
Non-Abelian symmetries of the half-infinite XXZ spin chain
Pascal Baseilhac, Samuel Belliard
The non-Abelian symmetries of the half-infinite XXZ spin chain for all possible types of integrable boundary conditions are classified. For each type of boundary conditions, an ana…
The alternating presentation of from Freidel-Maillet algebras
Pascal Baseilhac
An infinite dimensional algebra denoted that is isomorphic to a central extension of - the positive part of - has been recently propo…
New results in the XXZ open spin chain
Pascal Baseilhac
In this review, I describe a recent approach based on the representation theory of the Onsager algebra which is used to derive exact results for the XXZ open spin chain. The co…
Hidden symmetries in quantum field theories from extended complex numbers
Pascal Baseilhac
The 2-dimensional space-time sine-Gordon field theory is extended algebraically within the n-dimensional space of extended complex numbers. This field theory is constructed in term…