Invariants and reduced matrix elements associated with the Lie superalgebra gl(m|n)

DOI10.1063/1.4773573zbMath1290.17007arXiv1211.2857OpenAlexW2052494206WikidataQ60732447 ScholiaQ60732447MaRDI QIDQ5396256

Jason L. Werry, Phillip S. Isaac, Mark D. Gould

Publication date: 5 February 2014

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

Full work available at URL: https://arxiv.org/abs/1211.2857

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10)

Related Items

Invariants and reduced Wigner coefficients for quasi-triangular Hopf superalgebras ⋮ Representations of the Lie superalgebra $ \newcommand{\B}{\mathfrak{B}} {\B(\infty,\infty)}$ and parastatistics Fock spaces ⋮ Invariants and matrix elements of the quantum group $U_q[gl(n,\mathbb{C})$ revisited] ⋮ Matrix elements and duality for type 2 unitary representations of the Lie superalgebra gl(m|n) ⋮ A new integrable symplectic map by the binary nonlinearization to the super AKNS system ⋮ Reduced Wigner coefficients for Lie superalgebragl(m|n) corresponding to unitary representations and beyond ⋮ Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n) ⋮ The Z2×Z2-graded general linear Lie superalgebra

Cites Work

• Unnamed Item
• Unnamed Item
• Review of AdS/CFT integrability, chapter I.1: Spin chains in \({\mathcal{N}=4}\) super Yang-Mills
• Finite size properties of staggered \(U_q[sl(21)\) superspin chains]
• \(R\)-matrices and spectrum of vertex models based on superalgebras
• Continuum limit of the integrable \(sl(2/1)3-\bar 3\) superspin chain
• The \(\text{GL}(1| 1)\) WZW-model: from supergeometry to logarithmic CFT
• Essentially typical representations of Lie superalgebras \({\mathfrak gl}(n| m)\) in the Gel'fand-Tsetlin basis
• On the percolation BCFT and the crossing probability of Watts
• Determinant representations of correlation functions for the supersymmetric \(t\)-\(J\) model
• Irreducible finite-dimensional representations of Lie superalgebras gl(n,1) in the Gel'fand-Tsetlin basis
• On the tensor product of a finite and an infinite dimensional representation
• The \(N=4\) SYM integrable super spin chain
• The paraboson Fock space and unitary irreducible representations of the Lie superalgebra \({\mathfrak{osp}(1|2n)}\)
• A class of quadratic deformations of Lie superalgebras
• Polynomial identities for simple Lie superalgebras
• Eigenvalues of Casimir operators for the general linear and orthosymplectic Lie superalgebras
• Eigenvalues of Casimir operators for the general linear, the special linear, and the orthosymplectic Lie superalgebras
• Graded Lie algebras in mathematics and physics (Bose-Fermi symmetry)
• Tensor operators and projection techniques in infinite dimensional representations of semi-simple Lie algebras
• Classification of all star irreps of gl(m‖n)
• Branching rules for a class of typical and atypical representations of gl(m‖n)
• Branching rules for typical and atypical representations of gl(n|1)
• Finite-dimensional representations of the Lie superalgebra gl(2/2) in a gl(2)⊕gl(2) basis. II. Nontypical representations
• Casimir invariants, characteristic identities, and Young diagrams for color algebras and superalgebras
• Casimir invariants, characteristic identities, and tensor operators for ‘‘strange’’ superalgebras
• Characteristic identities for semi-simple Lie algebras
• Multiplicity-free Wigner coefficients for semisimple Lie groups. I. The U(n) pattern calculus
• Multiplicity-free Wigner coefficients for semisimple Lie groups. II. A pattern calculus for O(n)
• Finite-dimensional representations of the Lie superalgebra gl(2/2) in a gl(2)⊕gl(2) basis. I. Typical representations
• Casimir invariants and characteristic identities for generators of the general linear, special linear and orthosymplectic graded Lie algebras
• On an infinitesimal approach to semisimple Lie groups and raising and lowering operators of O(n) and U(n)
• Tensor operators for quantum groups and applications
• Semisimple graded Lie algebras
• On the structure of simple pseudo Lie algebras and their invariant bilinear forms
• Classification of all simple graded Lie algebras whose Lie algebra is reductive. I
• Wigner–Eckart theorem for tensor operators of graded Lie algebras
• Second Commutant Theorems in Enveloping Algebras
• The characteristic identities and reduced matrix elements of the unitary and orthogonal groups
• Eigenvalues of Casimir invariants of Uq (gl(m/n))
• Tensor operators and Wigner–Eckart theorem for the quantum superalgebraU_q[osp(1|2)]
• Wigner coefficients for a semisimple Lie group and the matrix elements of the O(n) generators
• On the matrix elements of the U(n) generators
• Eigenvalues of Casimir invariants for unitary irreps of
• Gel’fand–Zetlin basis and Clebsch–Gordan coefficients for covariant representations of the Lie superalgebra gl(m∣n)
• A q-superdimension formula for irreps of type I quantum superalgebras
• On the Representations of the Semisimple Lie Groups. II
• The parafermion Fock space and explicit \mathfrak{so}(2n+1) representations
• Canonical Unit Adjoint Tensor Operators in U(n)
• Characteristic Identities for Generators of GL(n), O(n) and Sp(n)
• WIGNER–ECKART THEOREM FOR TENSOR OPERATORS OF HOPF ALGEBRAS
• Relativistic wave equations
• Lie superalgebras

This page was built for publication: Invariants and reduced matrix elements associated with the Lie superalgebra gl(m|n)