Planar Rook Algebras and Tensor Representations of 𝔤𝔩(1 | 1)

DOI10.1080/00927872.2012.658533zbMath1269.05115arXiv1201.2482OpenAlexW2063104815MaRDI QIDQ2842309

Dongho Moon, Georgia M. Benkart

Publication date: 13 August 2013

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

Full work available at URL: https://arxiv.org/abs/1201.2482

zbMATH Keywords

general linear Lie superalgebra\(\mathfrak{gl}(1|1)\)-representationplanar rook algebraquantum enveloping algebra \(U_q (\mathfrak{gl}(1|1))\)

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Finite-dimensional groups and algebras motivated by physics and their representations (81R05)

Related Items (3)

A cubic defining algebra for the Links-Gould polynomial ⋮ The Alexander polynomial as quantum invariant of links ⋮ A categorification of \(\mathbf{U}_T(\mathfrak{sl}(1|1))\) and its tensor product representations

Cites Work

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• A polynomial invariant for knots via von Neumann algebras
• Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134)
• Crystal bases for the quantum superalgebra $U_q(\mathfrak {gl}(m,n))$
• Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem

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