Universal L operator and invariants of the quantum supergroup U q (gl(m/n))

DOI10.1063/1.529672zbMath0769.17011OpenAlexW2049965778MaRDI QIDQ4027870

Ruibin Zhang

Publication date: 9 March 1993

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

Full work available at URL: https://doi.org/10.1063/1.529672

zbMATH Keywords

invariantsquantum supergroupgraded Yang-Baxter equationspectral parameter-dependent solution

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) Lie groups (22E99)

Related Items (22)

General eigenvalue formula for Casimir invariants of type I quantum superalgebras ⋮ ON THE CONSTRUCTION OF CORRELATION FUNCTIONS FOR THE INTEGRABLE SUPERSYMMETRIC FERMION MODELS ⋮ On diagonal solutions of the reflection equation ⋮ Lax operator for the quantized orthosymplectic superalgebraU_q[osp(2|n)] ⋮ Eigenvalues of Casimir invariants of Uq (gl(m/n)) ⋮ The quantum super-Yangian and Casimir operators of \(U_ q{\mathfrak {gl}}(M| N)\) ⋮ Dual canonical bases for the quantum general linear supergroup ⋮ On the quantum affine superalgebra \(U_q(\widehat{\text{gl}}(2|2))\) at level one ⋮ On the Harish-Chandra homomorphism for quantum superalgebras ⋮ A Poincaré–Birkhoff–Witt commutator lemma for Uq[gl(m|n)] ⋮ A \(U_q(\widehat{gl}(2|2))_1\)-vertex model: creation algebras and quasi-particles. I ⋮ Algebraic Bethe ansatz for an integrable \(U_{q}[sl(n| m)\) vertex model with mixed representations] ⋮ A note on \(q\)-oscillator realizations of \(U_q(gl(M|N))\) for Baxter \(Q\)-operators ⋮ Braid group representations arising from quantum supergroups with arbitrary q and link polynomials ⋮ Other quantum relatives of the Alexander polynomial through the Links-Gould invariants ⋮ Lax operator for the quantised orthosymplectic superalgebra \(U_q[\text{osp} (m|n)\)] ⋮ Solutions to graded reflection equation of \(\mathrm{GL}\)-type ⋮ Finite size properties of staggered \(U_q[sl(21)\) superspin chains] ⋮ Representations of quantum affine superalgebras ⋮ The first fundamental theorem of invariant theory for the orthosymplectic supergroup ⋮ Finite dimensional irreducible representations of the quantum supergroup Uq (gl(m/n)) ⋮ Automatic construction of explicit R matrices for the one-parameter families of irreducible typical highest weight (\(\dot 0_m| \dot \alpha_n\)) representations of \(U_q[gl(m| n)\)]

Cites Work

• Quantum superalgebra \(U_q\mathrm{osp}(2,2)\)
• Solutions of the classical Yang-Baxter equation for simple superalgebras
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Quantum R matrix for the generalized Toda system
• Quantum Lie superalgebras and q-oscillators
• QUANTUM SUPERGROUPS AND SOLUTIONS OF THE YANG-BAXTER EQUATION
• Eigenvalues of Casimir operators for the general linear and orthosymplectic Lie superalgebras
• Graded tensor calculus
• Universal R matrices and invariants of quantum supergroups
• Invariants of the quantum supergroup U_q(gl(m/1))

This page was built for publication: Universal L operator and invariants of the quantum supergroup U q (gl(m/n))