scientific article
From MaRDI portal
Publication:2717204
zbMath0995.05148arXivmath/0406556MaRDI QIDQ2717204
Tatsuro Ito, Kenichiro Tanabe, Paul M. Terwilliger
Publication date: 9 October 2002
Full work available at URL: https://arxiv.org/abs/math/0406556
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Terwilliger algebra\(q\)-Racah polynomialAskey schemeAskey-Wilson algebraSerre relationsDolan-Grady relations
Association schemes, strongly regular graphs (05E30) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Canonical forms, reductions, classification (15A21)
Related Items
A generating function associated with the alternating elements in the positive part of Uq(sl^2) ⋮ Unnamed Item ⋮ Analogues of Lusztig's higher order relations for the q-Onsager algebra ⋮ Bidiagonal triads and the tetrahedron algebra ⋮ Compatibility and companions for Leonard pairs ⋮ A compact presentation for the alternating central extension of the positive part of Uq(sl^2) ⋮ Theq-Onsager algebra and multivariableq-special functions ⋮ Circular bidiagonal pairs ⋮ Using a q-shuffle algebra to describe the basic module V(Λ_0) for the quantized enveloping algebra Uq(sl^2) ⋮ On standard bases of irreducible modules of Terwilliger algebras of Doob schemes ⋮ The compact presentation for the alternating central extension of the \(q\)-Onsager algebra ⋮ A \(Q\)-polynomial structure associated with the projective geometry \(L_N (q)\) ⋮ A bivariate \(Q\)-polynomial structure for the non-binary Johnson scheme ⋮ Twisting finite-dimensional modules for the \(q\)-Onsager algebra \(\mathcal{O}_q\) via the Lusztig automorphism ⋮ Unnamed Item ⋮ Some q-Exponential Formulas Involving the Double Lowering Operator ψ for a Tridiagonal Pair (Research) ⋮ BIDIAGONAL PAIRS, THE LIE ALGEBRA 𝔰𝔩2, AND THE QUANTUM GROUP Uq(𝔰𝔩2) ⋮ LEONARD PAIRS AND THE ASKEY–WILSON RELATIONS ⋮ Dual polar graphs, a nil-DAHA of rank one, and non-symmetric dual \(q\)-Krawtchouk polynomials ⋮ ON THE WITT INDEX OF THE BILINEAR FORM DETERMINED BY A LEONARD PAIR ⋮ TD-pairs and the $q$-Onsager algebra ⋮ A deformed analogue of Onsager’s symmetry in the XXZ open spin chain ⋮ The classification of finite-dimensional irreducible modules of the Racah algebra ⋮ Exact spectrum of the XXZ open spin chain from theq-Onsager algebra representation theory ⋮ Introduction to Leonard pairs. ⋮ Entanglement of free fermions on Hadamard graphs ⋮ On quantum adjacency algebras of Doob graphs and their irreducible modules ⋮ Tridiagonal pairs and the quantum affine algebra \(U_q(\widehat{\text{sl}}_2)\). ⋮ Spin Leonard pairs ⋮ A family of tridiagonal pairs ⋮ Tridiagonal pairs of \(q\)-Racah type ⋮ Using Catalan words and a \(q\)-shuffle algebra to describe the Beck PBW basis for the positive part of \(U_q( \widehat{\mathfrak{sl}}_2)\) ⋮ Irreducible modules for the quantum affine algebra \(U_{q}(\mathfrak {\widehat{sl}_2})\) and its Borel subalgebra ⋮ Hessenberg pairs of linear transformations ⋮ Tridiagonal pairs of q-Racah type, the Bockting operator ψ, and L-operators for U_q(L(sl_2)) ⋮ Tridiagonal pairs of \(q\)-Serre type and their linear perturbations ⋮ The Lusztig automorphism of the \(q\)-Onsager algebra ⋮ Matrix units associated with the split basis of a Leonard pair ⋮ Linear transformations that are tridiagonal with respect to both eigenbases of a Leonard pair ⋮ The tetrahedron algebra and its finite-dimensional irreducible modules ⋮ 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 tetrahedron algebra, the Onsager algebra, and the \(\mathfrak{sl}_2\) loop algebra ⋮ The shape of some linear transformations ⋮ An infinite-dimensional \(\square_q\)-module obtained from the \(q\)-shuffle algebra for affine \(\mathfrak{sl}_2\) ⋮ Finite-dimensional irreducible \(\square_q\)-modules and their Drinfel'd polynomials ⋮ The \(q\)-deformed analogue of the Onsager algebra: beyond the Bethe ansatz approach ⋮ The split decomposition of a tridiagonal pair ⋮ Modular Leonard triples ⋮ Dual polar graphs, the quantum algebra \(U_q(\mathfrak{sl}_{2})\), and Leonard systems of dual \(q\)-Krawtchouk type ⋮ The algebra \(U_q(\mathfrak{sl}_2)\) in disguise ⋮ TD-pairs of type II with shape \(1,2,\dots,2,1\) ⋮ Two commuting operators associated with a tridiagonal pair ⋮ Krawtchouk polynomials, the Lie algebra \(\mathfrak{sl}_2\), and Leonard pairs ⋮ Tridiagonal pairs, alternating elements, and distance-regular graphs ⋮ On relative \(t\)-designs in polynomial association schemes ⋮ Leonard pairs from 24 points of view. ⋮ The structure of some linear transformations ⋮ Tridiagonal pairs of \(q\)-Racah type, the double lowering operator \({\psi}\), and the quantum algebra \(U_q(\mathfrak{sl}_2)\) ⋮ A bilinear form for tridiagonal pairs of \(q\)-Serre type ⋮ The shape of a tridiagonal pair. ⋮ Sharp tridiagonal pairs ⋮ Tridiagonal pairs of shape \((1,2,1)\) ⋮ Evaluation modules for the \(q\)-tetrahedron algebra ⋮ The Terwilliger polynomial of a \(Q\)-polynomial distance-regular graph and its application to pseudo-partition graphs ⋮ Towards a classification of the tridiagonal pairs ⋮ An action of the tetrahedron algebra on the standard module for the Hamming graphs and Doob graphs ⋮ Tridiagonal pairs of Krawtchouk type ⋮ A conjecture concerning the \(q\)-Onsager algebra ⋮ Leonard triples, the Racah algebra, and some distance-regular graphs of Racah type ⋮ Irreducible modules for the quantum affine algebra \(U_{q}(\mathfrak g)\) and its Borel subalgebra \(U_{q}(\mathfrak g)^{\geqslant 0}\) ⋮ Leonard triples of \(q\)-Racah type and their pseudo intertwiners ⋮ Nonsymmetric Askey-Wilson polynomials and \(Q\)-polynomial distance-regular graphs ⋮ The structure of a tridiagonal pair ⋮ The switching element for a Leonard pair ⋮ The alternating central extension of the \(q\)-Onsager algebra ⋮ The \(q\)-Onsager algebra and the positive part of \(U_q(\hat{\mathfrak{sl}}_2)\) ⋮ Bidiagonal triples ⋮ The \(q\)-Onsager algebra and the universal Askey-Wilson algebra ⋮ Cyclic tridiagonal pairs, higher order Onsager algebras and orthogonal polynomials ⋮ 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 Terwilliger algebra of a distance-regular graph of negative type ⋮ Tridiagonal pairs and the \(\mu \)-conjecture ⋮ The traces associated with a sharp tridiagonal system ⋮ The quantum adjacency algebra and subconstituent algebra of a graph ⋮ A new current algebra and the reflection equation ⋮ A refinement of the split decomposition of a tridiagonal pair ⋮ Tridiagonal pairs of height one ⋮ Tridiagonal pairs of \(q\)-Racah type and the \(\mu \)-conjecture ⋮ Thin Hessenberg pairs ⋮ Two linear transformations each tridiagonal with respect to an eigenbasis of the other; comments on the parameter array ⋮ A duality between pairs of split decompositions for a Q-polynomial distance-regular graph ⋮ A classification of sharp tridiagonal pairs ⋮ Some properties of sharp Hessenberg pairs ⋮ Mock tridiagonal systems ⋮ The quantum algebra \(U_q(\mathfrak{sl}_2)\) and its equitable presentation ⋮ Generalized \(q\)-Onsager algebras and boundary affine Toda field theories ⋮ Two linear transformations each tridiagonal with respect to an eigenbasis of the other: comments on the split decomposition ⋮ Tridiagonal pairs and the Askey--Wilson relations ⋮ The determinant of \(AA^{*} - A^{*}A\) for a Leonard pair \(A,A^{*}\) ⋮ Tridiagonal pairs of \(q\)-Racah-type and the \(q\)-tetrahedron algebra ⋮ Double lowering operators on polynomials ⋮ \(p\)-inverting pairs of linear transformations and the \(q\)-tetrahedron algebra ⋮ A bilinear form relating two Leonard systems ⋮ The attenuated space poset \(\mathcal{A}_q(N, M)\) ⋮ \(Q\)-polynomial distance-regular graphs with \(a_1=0\) and \(a_2\neq 0\) ⋮ Affine transformations of a sharp tridiagonal pair ⋮ The Classification of Finite-Dimensional Irreducible Modules of Bannai/Ito Algebra ⋮ New proofs of the Assmus-Mattson theorem based on the Terwilliger algebra ⋮ Leonard triples and hypercubes ⋮ Distance-regular graphs of \(q\)-Racah type and the \(q\)-tetrahedron algebra ⋮ The Terwilliger algebra of the Johnson scheme \(J(N, D)\) revisited from the viewpoint of group representations ⋮ Transition maps between the 24 bases for a Leonard pair ⋮ Tridiagonal pairs and the \(q\)-tetrahedron algebra ⋮ Linking the special orthogonal algebra \(\mathfrak{so}_4\) and the tetrahedron algebra \(\boxtimes \) ⋮ Commutative association schemes ⋮ The Rahman polynomials and the Lie algebra $\mathfrak{sl}_{3}(\mathbb{C})$ ⋮ On the shape of a tridiagonal pair ⋮ Circular Hessenberg pairs ⋮ Two linear transformations each tridiagonal with respect to an eigenbasis of the other; the TD-D canonical form and the LB-UB canonical form ⋮ A bispectral q-hypergeometric basis for a class of quantum integrable models ⋮ Leonard pairs having zero-diagonal TD-TD form ⋮ Some trace formulae involving the split sequences of a Leonard pair