He, Yuxing; Abdukadir, Obul Gröbner-Shirshov pair of irreducible modules over quantum group \(U_q(D_4)\). (Chinese. English summary) Zbl 1474.17016 Math. Pract. Theory 51, No. 1, 204-213 (2021). Summary: We first compute a Gröbner-Shirshov pair of the irreducible module \(V_q(\lambda)\) over the quantum group \(U_q(D_4)\) by using the known Gröbner-Shirshov basis of the quantum group \(U_q(D_4)\) and the double free module method of Chibrikov, then define a suitable version \(U'_q(D_4)\) of \(U_q(D_4)\) and by specializing \(U'_q(D_4)\) at \(q = 1\), we get a Gröbner-Shirshov pair of the irreducible module \(V (\lambda)\) over the universal enveloping algebra \(U (D_4)\) of simple Lie algebra of type \(D_4\). MSC: 17B37 Quantum groups (quantized enveloping algebras) and related deformations 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 17A61 Gröbner-Shirshov bases in nonassociative algebras Keywords:quantum group; Gröbner-Shirshov pair; irreducible module; compositions PDFBibTeX XMLCite \textit{Y. He} and \textit{O. Abdukadir}, Math. Pract. Theory 51, No. 1, 204--213 (2021; Zbl 1474.17016)