Young tableaux and crystal base for \(U_q(\text{osp}(1|2n))\)
type: Item
instance of: scholarly article
title: Young tableaux and crystal base for \(U_q(\text{osp}(1|2n))\)
zbMATH Open document ID: 1186.17009
author: Junli Liu
author: Shilin Yang
published in: Science China. Mathematics
publication date: 2010-04-13T00:00:00Z
review text: The authors introduce a class of quantized enveloping superalgebra \(U_q(\text{osp}(1|2n))\) corresponding to the Lie superalgebra \(\text{osp}(1|2n)\). The authors also give a relation of crystal graph of finete-dimensional irreducible modules of \(U_q(\text{osp}(1|2n))\) in terms of semistandard Young tableaux satisfying some additional conditions. The authors also describe a combinatorial rule of decomposing the tensor product of finite-dimensional integral modules into a direct sum of irreducible submodules, and establish the generalized Littlewood-Richardson rule for tensor product of crystal graphs.
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 05E10
zbMATH DE Number: 5692420
MaRDI profile type: Publication
full work available at URL: s11425-009-0080-0
OpenAlex ID: W2167425489
cites work: Tensor product representations for orthosymplectic Lie superalgebras
cites work: Q4537716
cites work: Crystal bases for Kac-Moody superalgebras
cites work: Crystal bases and tensor product decompositions of \(U_ q(G_ 2)\)- modules
cites work: On crystal bases of the \(q\)-analogue of universal enveloping algebras
cites work: Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
cites work: Q4265608
cites work: Canonical Bases Arising from Quantized Enveloping Algebras
cites work: Crystal bases for \(U_q(osp (1,2r))\)
cites work: Crystal base and a generalization of the Littlewood-Richardson rule for the classical Lie algebras
cites work: Integrable representations of \(U_q(\text{osp}(1,2n))\)
DOI: 10.1007/S11425-009-0080-0
description: scientific article; zbMATH DE number 5692420