Unitarity and complete reducibility of certain modules over quantized affine Lie algebras

DOI10.1063/1.530249zbMath0795.17009arXivhep-th/9303096OpenAlexW3103142606WikidataQ60732532 ScholiaQ60732532MaRDI QIDQ4276817

Yao-Zhong Zhang, Mark D. Gould

Publication date: 19 April 1994

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9303096

zbMATH Keywords

reducibilityintegrable modulesunitarityuniversal \(R\)-matrixquantized affine Lie algebra

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) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10)

Related Items

Casimir invariants for quantized affine Lie algebras ⋮ General eigenvalue formula for Casimir invariants of type I quantum superalgebras ⋮ Invariants and matrix elements of the quantum group $U_q[gl(n,\mathbb{C})$ revisited] ⋮ Quantum affine Lie algebras, Casimir invariants, and diagonalization of the braid generator ⋮ Classification of finite dimensional unitary irreps for U q[gl(m‖n)] ⋮ Quantised affine algebras and parameter-dependent R-matrices

Cites Work

• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Quantum R matrix for the generalized Toda system
• Quantum deformations of certain simple modules over enveloping algebras
• Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra
• Quantum group invariants and link polynomials
• Quantum affine algebras and holonomic difference equations
• Invariants of 3-manifolds via link polynomials and quantum groups
• QUANTUM SUPERGROUPS AND SOLUTIONS OF THE YANG-BAXTER EQUATION
• Classification of all star irreps of gl(m‖n)
• Vertex representations of quantum affine algebras
• Generalized Gel’fand invariants and characteristic identities for quantum groups

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