A classification of sharp tridiagonal pairs

DOI10.1016/J.LAA.2011.03.032zbMath1225.15015arXiv1001.1812OpenAlexW2070023863MaRDI QIDQ551310

Tatsuro Ito, Nomura, Kazumasa, Paul M. Terwilliger

Publication date: 15 July 2011

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.1812

zbMATH Keywords

linear transformationstridiagonal pairLeonard pair\(q\)-Racah polynomials

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Linear transformations, semilinear transformations (15A04) Canonical forms, reductions, classification (15A21)

Related Items (25)

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 ⋮ Unnamed Item ⋮ Analogues of Lusztig's higher order relations for the q-Onsager algebra ⋮ Finite-dimensional irreducible \(\square_q\)-modules and their Drinfel'd polynomials ⋮ Circular bidiagonal pairs ⋮ The algebra \(U_q(\mathfrak{sl}_2)\) in disguise ⋮ TD-pairs of type II with shape \(1,2,\dots,2,1\) ⋮ A \(Q\)-polynomial structure associated with the projective geometry \(L_N (q)\) ⋮ Two commuting operators associated with a tridiagonal pair ⋮ Twisting finite-dimensional modules for the \(q\)-Onsager algebra \(\mathcal{O}_q\) via the Lusztig automorphism ⋮ Unnamed Item ⋮ Tridiagonal pairs, alternating elements, and distance-regular graphs ⋮ Evaluation modules for the \(q\)-tetrahedron algebra ⋮ 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 quantum adjacency algebra and subconstituent algebra of a graph ⋮ TD-pairs and the $q$-Onsager algebra ⋮ Affine transformations of a sharp tridiagonal pair ⋮ The Rahman polynomials and the Lie algebra $\mathfrak{sl}_{3}(\mathbb{C})$ ⋮ Circular Hessenberg pairs ⋮ A bispectral q-hypergeometric basis for a class of quantum integrable models ⋮ q-Inverting pairs of shape 1, 2, 1

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