Gr?bner-Shirshov bases of irreducible modules over the quantum group U_q(F_4)

摘要

In this paper, we construct a Gr?bner-Shirshov bases for the finite dimensional irreducible module Vq (λ) of the quantum group U_q (F4) by using the double free module method and the known Gr?bner-Shirshov bases of U_q (F4). Then, by specializing a suitable version of U_q (F4) at q = 1, we get a Gr?bner-Shirshov bases of the universal enveloping algebra U(F4) of the simple Lie algebra of type F4 and the finite dimensional irreducible U(F4)?module V(λ).