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

Abstract

We consider the quantum algebra $U_q({\mathfrak{sl}}_2)$ with $q$ not a root of unity. We describe the finite-dimensional irreducible $U_q({\mathfrak{sl}}_2)$-modules from the point of view of the equitable presentation.

47 pages

References in corpus (5)

• The Universal Askey-Wilson Algebra and the Equitable Presentation of $U_q({\mathfrak{sl}}_2)$
• The quantum algebra $U_q(s{l}_2)$ and its equitable presentation
• Dual polar graphs, the quantum algebra U_q(sl_2), and Leonard systems of dual q-Krawtchouk type
• Bidiagonal pairs, the Lie algebra sl_2, and the quantum group U_q(sl_2)
• $q$-Inverting pairs of linear transformations and the $q$-tetrahedron algebra

Cited by in corpus (6)

• Linear transformations that are tridiagonal with respect to the three decompositions for an LR triple
• Billiard Arrays and finite-dimensional irreducible $U_q({\mathfrak{sl}}_2)$-modules
• Evaluation modules for the $q$-tetrahedron algebra
• An LR pair that can be extended to an LR triple
• The algebra $U_q({\mathfrak{sl}}_2)$ in disguise
• The Lusztig automorphism of $U_q({\mathfrak{sl}}_2)$ from the equitable point of view