Raising/Lowering Maps and Modules for the Quantum Affine Algebra

DOI10.1080/00927870701302156zbMath1129.17010arXivmath/0506629OpenAlexW2093771494MaRDI QIDQ5756470

Darren Funk-Neubauer

Publication date: 4 September 2007

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0506629

zbMATH Keywords

quantum affine algebraraising operatorsfinite-dimensional modulesbasic representation

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Quantum groups (quantized function algebras) and their representations (20G42)

Related Items (9)

Bidiagonal triads and the tetrahedron algebra ⋮ Unnamed Item ⋮ Sharp tridiagonal pairs ⋮ Towards a classification of the tridiagonal pairs ⋮ The structure of a tridiagonal pair ⋮ Bidiagonal triples ⋮ BIDIAGONAL PAIRS, THE LIE ALGEBRA 𝔰𝔩₂, AND THE QUANTUM GROUP U_q(𝔰𝔩₂) ⋮ Tridiagonal pairs and the \(q\)-tetrahedron algebra ⋮ On the shape of a tridiagonal pair

Cites Work

• Unnamed Item
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• Quantum affine algebras
• Finite-dimensional modules of quantum affine algebras.
• The shape of a tridiagonal pair.
• Fractional spin through quantum affine algebras with vanishing central charge
• Irreducible modules for the quantum affine algebra \(U_{q}(\mathfrak {\widehat{sl}_2})\) and its Borel subalgebra
• Tridiagonal pairs and the quantum affine algebra \(U_q(\widehat{\text{sl}}_2)\).
• Crystal bases of the Fock space representations and string functions
• Kac-Moody Lie Algebras and Related Topics

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