Gröbner-Shirshov bases of irreducible modules over the quantum group \(U_q(F_4)\) (Q2516006)

A Gröbner-Shirshov basis of the finite dimensional irreducible module \(V_q(\lambda)\) of the quantum group \(U_q(F_4)\) is given which provides a computational approach to the study of the structure of \(U_q(F_4)\) and its representation \(V_q(\lambda)\). By specializing a suitable version of \(U_q(F_4)\) at \(q=1\), Gröbner-Shirshov bases of the universal enveloping algebra \(U(F_4)\) of the simple Lie algebra of type \(F_4\) and the finite dimensional irreducible \(U(F_4)\)-module \(V(\lambda)\) are obtained.