Finite-dimensional irreducible \(U_q(\mathfrak{sl}_2)\)-modules from the equitable point of view

DOI10.1016/j.laa.2013.03.022zbMath1354.17012arXiv1303.6134OpenAlexW2075323857MaRDI QIDQ2637156

Paul M. Terwilliger

Publication date: 19 February 2014

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

Full work available at URL: https://arxiv.org/abs/1303.6134

zbMATH Keywords

quantum groupflagdual spaceLeonard pairquantum universal enveloping algebra

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37)

Related Items

Bidiagonal triads and the tetrahedron algebra ⋮ The algebra \(U_q(\mathfrak{sl}_2)\) in disguise ⋮ Some \(q\)-exponential formulas for finite-dimensional \(\square_q\)-modules ⋮ Billiard arrays and finite-dimensional irreducible \(U_q(\mathfrak{sl}_2)\)-modules ⋮ The Lusztig automorphism of Uq(𝔰𝔩2) from the equitable point of view ⋮ Twisting finite-dimensional modules for the \(q\)-Onsager algebra \(\mathcal{O}_q\) via the Lusztig automorphism ⋮ Unnamed Item ⋮ An LR pair that can be extended to an LR triple ⋮ Upper triangular matrices and billiard arrays ⋮ Evaluation modules for the \(q\)-tetrahedron algebra ⋮ Lowering-raising triples and \(U_q(\mathfrak{sl}_2)\) ⋮ Linear transformations that are tridiagonal with respect to the three decompositions for an LR triple ⋮ Unnamed Item ⋮ Leonard pairs and quantum algebra \(U_q(sl_{2})\) ⋮ Bidiagonal triples ⋮ Equitable presentations for multiparameter quantum groups ⋮ Tridiagonal pairs of \(q\)-Racah-type and the \(q\)-tetrahedron algebra ⋮ 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 \({\mathfrak{sl}_2}\)
• Finite dimensional modules for the \(q\)-tetrahedron algebra
• \(p\)-inverting pairs of linear transformations and the \(q\)-tetrahedron algebra
• Distance-regular graphs and the \(q\)-tetrahedron algebra
• Distance-regular graphs of \(q\)-Racah type and the \(q\)-tetrahedron algebra
• Tridiagonal pairs and the \(q\)-tetrahedron algebra
• Leonard pairs from 24 points of view.
• Dual polar graphs, the quantum algebra \(U_q(\mathfrak{sl}_{2})\), and Leonard systems of dual \(q\)-Krawtchouk type
• Finite-dimensional simple Poisson modules
• Tridiagonal pairs and the quantum affine algebra \(U_q(\widehat{\text{sl}}_2)\).
• 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
• 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
• Theq-Tetrahedron Algebra and Its Finite Dimensional Irreducible Modules
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