Unitary highest weight representations of quantum general linear superalgebra

DOI10.1016/j.jalgebra.2008.02.040zbMath1168.17011OpenAlexW2059152047MaRDI QIDQ834849

Ruibin Zhang, Yue Zhu Wu

Publication date: 27 August 2009

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2008.02.040

zbMATH Keywords

quantum groupunitary representationLie superalgebraFock space

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37)

Related Items (7)

Super \(q\)-Howe duality and web categories ⋮ The first and second fundamental theorems of invariant theory for the quantum general linear supergroup ⋮ Mixed quantum skew Howe duality and link invariants of type \(A\) ⋮ The first fundamental theorem of invariant theory for the orthosymplectic supergroup ⋮ Howe duality for quantum queer superalgebras ⋮ Polynomial link invariants and quantum algebras ⋮ Geometric Howe dualities of finite type

Cites Work

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• On the Segal-Shale-Weil representations and harmonic polynomials
• The theory of Lie superalgebras. An introduction
• Structure and representations of the quantum general linear supergroup
• Integrable representations of \(U_q(\text{osp}(1,2n))\)
• Finite-dimensional representations of the quantum superalgebra \(U_ q[gl(n/m)\) and related \(q\)-identities]
• Unitarity of highest-weight modules for quantum groups
• Howe duality and combinatorial character formula for orthosymplectic Lie superalgebras.
• Character formula for infinite-dimensional unitarizable modules of the general linear super\-algebra.
• Classification of all star irreps of gl(m‖n)
• Remarks on Classical Invariant Theory
• Finite dimensional irreducible representations of the quantum supergroup Uq (gl(m/n))
• Classification of finite dimensional unitary irreps for U q[gl(m‖n)]
• Crystal bases for the quantum superalgebra $U_q(\mathfrak {gl}(m,n))$
• Quasi-finite modules for Lie superalgebras of infinite rank
• Lie superalgebras

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