Billiard arrays and finite-dimensional irreducible \(U_q(\mathfrak{sl}_2)\)-modules

DOI10.1016/j.laa.2014.08.002zbMath1352.17021arXiv1408.0143OpenAlexW2041635505MaRDI QIDQ406487

Paul M. Terwilliger

Publication date: 8 September 2014

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

Full work available at URL: https://arxiv.org/abs/1408.0143

zbMATH Keywords

quantum groupLie algebraflagquantum enveloping algebra

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Canonical forms, reductions, classification (15A21)

Related Items (8)

Bidiagonal triads and the tetrahedron algebra ⋮ Some \(q\)-exponential formulas for finite-dimensional \(\square_q\)-modules ⋮ The Lusztig automorphism of Uq(𝔰𝔩2) from the equitable point of view ⋮ An LR pair that can be extended to an LR triple ⋮ Upper triangular matrices and billiard arrays ⋮ Lowering-raising triples and \(U_q(\mathfrak{sl}_2)\) ⋮ Linear transformations that are tridiagonal with respect to the three decompositions for an LR triple ⋮ Freidel-Maillet type presentations of \(U_q(sl_2)\)

Cites Work

• The universal Askey-Wilson algebra and the equitable presentation of \(U_{q}(sl_{2})\)
• The equitable basis for \({\mathfrak{sl}_2}\)
• The classification of Leonard triples of QRacah type
• The tetrahedron algebra, the Onsager algebra, and the \(\mathfrak{sl}_2\) loop algebra
• Dual polar graphs, the quantum algebra \(U_q(\mathfrak{sl}_{2})\), and Leonard systems of dual \(q\)-Krawtchouk type
• Tridiagonal pairs and the quantum affine algebra \(U_q(\widehat{\text{sl}}_2)\).
• Evaluation modules for the \(q\)-tetrahedron algebra
• The quantum algebra \(U_q(\mathfrak{sl}_2)\) and its equitable presentation
• The equitable presentation for the quantum group associated with a symmetrizable Kac-Moody algebra
• Finite-dimensional irreducible \(U_q(\mathfrak{sl}_2)\)-modules from the equitable point of view
• Leonard pairs associated with the equitable generators of the quantum algebraU_q(sl₂)
• TWO NON-NILPOTENT LINEAR TRANSFORMATIONS THAT SATISFY THE CUBIC q-SERRE RELATIONS
• BIDIAGONAL PAIRS, THE LIE ALGEBRA 𝔰𝔩₂, AND THE QUANTUM GROUP U_q(𝔰𝔩₂)
• Theq-Tetrahedron Algebra and Its Finite Dimensional Irreducible Modules
• Introduction to Lie Algebras and Representation Theory
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