MIXED TENSOR REPRESENTATIONS AND RATIONAL REPRESENTATIONS FOR THE GENERAL LINEAR LIE SUPERALGEBRAS

DOI10.1081/AGB-120013185zbMath1035.17013OpenAlexW2069771005MaRDI QIDQ4532328

Dongho Moon, Chanyoung Lee Shader

Publication date: 8 September 2003

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

Full work available at URL: https://doi.org/10.1081/agb-120013185

zbMATH Keywords

mixed tensor representationsLie superalgebra \(\text{gl}(m, n)\)

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10)

Related Items

Affine oriented Frobenius Brauer categories ⋮ Affine walled Brauer algebras and super Schur-Weyl duality ⋮ Mixed Schur-Weyl-Sergeev duality for queer Lie superalgebras ⋮ Supersymmetric polynomials and the center of the walled Brauer algebra ⋮ Bimodule structure of the mixed tensor product over \(\mathcal{U}_q s \ell(2 | 1)\) and quantum walled Brauer algebra ⋮ Gradings on walled Brauer algebras and Khovanov's arc algebra ⋮ Affine walled Brauer-Clifford superalgebras ⋮ Mixed Tensor Representations of Quantum Superalgebra _q(gl(m,n)) ⋮ Quantum walled Brauer-Clifford superalgebras

Cites Work

• Rational tableaux and the tensor algebra of \(gl_ n\)
• On the decomposition of the tensor algebra of the classical Lie algebras
• Tensor product representations of general linear groups and their connections with Brauer algebras
• Hook Young diagrams with applications to combinatorics and to representations of Lie superalgebras
• On the decomposition of tensor products of the representations of the classical groups: By means of the universal characters
• Characters of the centralizer algebras of mixed tensor representations of \(GL(r,\mathbb{C})\) and the quantum group \({\mathcal U}_ q(gl(r,\mathbb{C}))\)
• Complex parameters for the representations of some superalgebras
• A character formula for singly atypical modules of the lie superalgebra sl(m/n)