Abstract
In this paper, we construct a Gröbner-Shirshov bases for the finite dimensional irreducible module \(V_q(\lambda )\) of the quantum group \(U_q(F_4)\) by using the double free module method and the known Gröbner-Shirshov bases of \(U_q(F_4).\) Then, by specializing a suitable version of \(U_q(F_4)\) at \(q=1,\) we get a 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 \(V(\lambda )\).
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We are very grateful for the useful comments and suggestions for the referee.
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Supported by National Natural Science Foundation of China (Grant No. 11061033, No. 11361056).
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Zikerya, A., Obul, A. Gröbner-Shirshov bases of irreducible modules over the quantum group \(U_q(F_4)\) . Rend. Circ. Mat. Palermo 64, 309–322 (2015). https://doi.org/10.1007/s12215-015-0201-2
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DOI: https://doi.org/10.1007/s12215-015-0201-2