Finite-dimensional representations of the quantum superalgebra \(U_ q[gl(n/m)]\) and related \(q\)-identities
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Publication:1344493
DOI10.1007/BF02112320zbMath0853.17016arXivhep-th/9306149MaRDI QIDQ1344493
Tchavdar D. Palev, Joris Van der Jeugt, Neli I. Stoilova
Publication date: 13 February 1995
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/hep-th/9306149
generatorstypical representations\(q\)-number identitiesGel'fand-Zetlin basisquantum superalgebra \(U_ q [gl(n/m)\)]
Quantum groups (quantized enveloping algebras) and related deformations (17B37) Superalgebras (17A70)
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Cites Work
- Unnamed Item
- An analogue of P.B.W. theorem and the universal R-matrix for \(U_ h\mathfrak{sl}(N+1)\)
- Universal R-matrix of the quantum superalgebra osp(2\(| 1)\)
- 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
- \(q\)-oscillator realizations of the quantum superalgebras \(sl_ q(m,n)\) and \(osp_ q(m,2n)\)
- Finite-dimensional irreducible representations of the quantum superalgebra \(U_ q[gl(n/1)\)]
- Universal \(R\)-matrix for quantized (super)algebras
- Universal R-matrices for quantum groups associated to simple Lie superalgebras
- On the defining relations of quantum superalgebras
- Serre-type relations for special linear Lie superalgebras
- The theory of Lie superalgebras. An introduction
- Quantized enveloping algebras associated with simple Lie superalgebras and their universal \(R\)-matrices
- QUANTUM SUPERGROUPS AND SOLUTIONS OF THE YANG-BAXTER EQUATION
- Irreducible finite-dimensional representations of the Lie superalgebra gl(n/1) in a Gel’fand–Zetlin basis
- On the composition factors of Kac modules for the Lie superalgebras sl(m/n)
- Finite dimensional irreducible representations of the quantum supergroup Uq (gl(m/n))
- Finite-dimensional representations of the quantum superalgebra Uq(gl(3/2)) in a reduced Uq(gl(3/2)) contains/implies Uq(gl(3/1)) contains/implies Uq(gl(3)) basis
- Character formulas for irreducible modules of the Lie superalgebras sl(m/n)
- A character formula for singly atypical modules of the lie superalgebra sl(m/n)
- Lie superalgebras