Young tableaux and crystal base for \(U_q(\text{osp}(1|2n))\)
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.
scientific article; zbMATH DE number 5692420