Tridiagonal pairs and the \(q\)-tetrahedron algebra
From MaRDI portal
Publication:1030753
DOI10.1016/j.laa.2009.03.045zbMath1206.17013arXiv0806.0901OpenAlexW2963254423MaRDI QIDQ1030753
Publication date: 2 July 2009
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0806.0901
Quantum groups (quantized enveloping algebras) and related deformations (17B37) Infinite-dimensional Lie (super)algebras (17B65) Canonical forms, reductions, classification (15A21) Ring-theoretic aspects of quantum groups (16T20)
Related Items
Tridiagonal pairs of \(q\)-Racah type, Finite-dimensional irreducible \(U_q(\mathfrak{sl}_2)\)-modules from the equitable point of view, Bidiagonal triads and the tetrahedron algebra, Unnamed Item, Some q-Exponential Formulas Involving the Double Lowering Operator ψ for a Tridiagonal Pair (Research), Tridiagonal pairs of \(q\)-Racah type, the double lowering operator \({\psi}\), and the quantum algebra \(U_q(\mathfrak{sl}_2)\), Evaluation modules for the \(q\)-tetrahedron algebra, Bidiagonal triples, BIDIAGONAL PAIRS, THE LIE ALGEBRA 𝔰𝔩2, AND THE QUANTUM GROUP Uq(𝔰𝔩2), A classification of sharp tridiagonal pairs, Mock tridiagonal systems, HOW TO SHARPEN A TRIDIAGONAL PAIR, Finite dimensional modules for the \(q\)-tetrahedron algebra, Leonard pairs having zero-diagonal TD-TD form
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Some trace formulae involving the split sequences of a Leonard pair
- Matrix units associated with the split basis of a Leonard pair
- Balanced Leonard pairs
- Linear transformations that are tridiagonal with respect to both eigenbases of a Leonard pair
- Normalized Leonard pairs and Askey--Wilson relations
- The tetrahedron algebra and its finite-dimensional irreducible modules
- An integrable structure related with tridiagonal algebras
- The tetrahedron algebra, the Onsager algebra, and the \(\mathfrak{sl}_2\) loop algebra
- The split decomposition of a tridiagonal pair
- Modular Leonard triples
- A bilinear form for tridiagonal pairs of \(q\)-Serre type
- Sharp tridiagonal pairs
- Tridiagonal pairs of shape \((1,2,1)\)
- Towards a classification of the tridiagonal pairs
- The structure of a tridiagonal pair
- \(p\)-inverting pairs of linear transformations and the \(q\)-tetrahedron algebra
- Leonard pairs from 24 points of view.
- The shape of a tridiagonal pair.
- Leonard pairs and the \(q\)-Racah polynomials
- Two linear transformations each tridiagonal with respect to an eigenbasis of the other; comments on the parameter array
- 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
- Introduction to Leonard pairs.
- A family of tridiagonal pairs
- Irreducible modules for the quantum affine algebra \(U_{q}(\mathfrak {\widehat{sl}_2})\) and its Borel subalgebra
- Tridiagonal pairs and the quantum affine algebra \(U_q(\widehat{\text{sl}}_2)\).
- Spin Leonard pairs
- Tridiagonal pairs of Krawtchouk type
- Irreducible modules for the quantum affine algebra \(U_{q}(\mathfrak g)\) and its Borel subalgebra \(U_{q}(\mathfrak g)^{\geqslant 0}\)
- The switching element for a Leonard pair
- A refinement of the split decomposition of a tridiagonal pair
- Tridiagonal pairs of height one
- The determinant of \(AA^{*} - A^{*}A\) for a Leonard pair \(A,A^{*}\)
- Three mutually adjacent Leonard 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
- TWO RELATIONS THAT GENERALIZE THE Q-SERRE RELATIONS AND THE DOLAN-GRADY RELATIONS
- The universal central extension of the three-point $\mathfrak {sl}_2$ loop algebra
- Affine transformations of a Leonard pair
- TWO NON-NILPOTENT LINEAR TRANSFORMATIONS THAT SATISFY THE CUBIC q-SERRE RELATIONS
- A family of tridiagonal pairs related to the quantum affine algebra U_q(sl_2)
- LEONARD PAIRS AND THE ASKEY–WILSON RELATIONS
- Finite-Dimensional Irreducible Modules for the Three-Point 2 Loop Algebra
- Theq-Tetrahedron Algebra and Its Finite Dimensional Irreducible Modules
- The $S_4$-action on tetrahedron algebra
- A family of tridiagonal pairs and related symmetric functions
- Raising/Lowering Maps and Modules for the Quantum Affine Algebra
- Two linear transformations each tridiagonal with respect to an eigenbasis of the other