The \(gl(M| N)\) super Yangian and its finite-dimensional representations

DOI10.1007/BF00312673zbMath0861.17020arXivq-alg/9507029MaRDI QIDQ1922514

Ruibin Zhang

Publication date: 6 November 1996

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

Full work available at URL: https://arxiv.org/abs/q-alg/9507029

zbMATH Keywords

Hopf algebrashighest weight representationsirreducible representationsPoincaré-Birkhoff-Witt theoremLie superalgebra \(gl(m,n)\)super Yangian

Mathematics Subject Classification ID

Applications of Lie (super)algebras to physics, etc. (17B81) Graded Lie (super)algebras (17B70) ``Super (or ``skew) structure (16W55)

Related Items

A note on odd reflections of super Yangian and Bethe ansatz, Completeness of Wronskian Bethe equations for rational \(\mathfrak{gl}_{\mathsf{m}|\mathsf{n}}\) spin chains, Unnamed Item, Yangian of \(\mathrm{AdS}_3 /\mathrm{CFT}_2\) and its deformation, R -matrix presentation for super-Yangians Y(osp(m|2n)), Twisted super-Yangians and their representations, New quiver-like varieties and Lie superalgebras, Representations of the super Yangians of types \(A\) and \(C\), Representations of the Yangians associated with Lie superalgebras \(\mathfrak{osp}(1|2n)\), Representations of quantum affine superalgebras, Structure and representations on the quantum supergroup OSPq(2|2n), Gauss decomposition of the Yangian \(Y({\mathfrak{gl}}_{m|n})\), The exact \(S\)-matrix for an \(\text{osp}(2| 2)\) disordered system., PBWD bases and shuffle algebra realizations for \(U_v(L\mathfrak{sl}_n)\), \(U_{v_1,v_2} (L\mathfrak{sl}_n)\), \(U_v (L\mathfrak{sl}(m|n))\) and their integral forms, New compact construction of eigenstates for supersymmetric spin chains, Finite-dimensional irreducible representations of twisted Yangians, Unnamed Item, Gelfand-Tsetlin bases of representations for super Yangian and quantum affine superalgebra, Odd reflections in the Yangian associated with \(\mathfrak{gl}(m|n)\), Representations of the Yangian of a Lie superalgebra of type $ A(m,n)$

Cites Work

• Quantum Berezinian and the classical Capelli identity
• The Yangians, Bethe Ansatz and combinatorics
• A new interpretation of Gelfand-Tsetlin bases
• Gelfand-Tsetlin basis for representations of Yangians
• The quantum super-Yangian and Casimir operators of \(U_ q{\mathfrak {gl}}(M| N)\)
• The cohomology structure of an associative ring
• Finite dimensional irreducible representations of the quantum supergroup Uq (gl(m/n))
• Representations of super Yangian
• Lie superalgebras