Upper triangular matrices and billiard arrays

DOI10.1016/j.laa.2015.12.023zbMath1329.05304arXiv1508.04456OpenAlexW2963204754MaRDI QIDQ905741

Yang Yang

Publication date: 28 January 2016

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

Full work available at URL: https://arxiv.org/abs/1508.04456

zbMATH Keywords

quantum groupflagequitable presentationupper triangular matrixbilliard array

Mathematics Subject Classification ID

Canonical forms, reductions, classification (15A21)

Related Items

Bidiagonal triads and the tetrahedron algebra, Unnamed Item

Cites Work

• Billiard arrays and finite-dimensional irreducible \(U_q(\mathfrak{sl}_2)\)-modules
• The universal Askey-Wilson algebra and the equitable presentation of \(U_{q}(sl_{2})\)
• The classification of Leonard triples of QRacah type
• 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