Abstract
Let \(\mathfrak{g}\) be a classical complex simple Lie algebra and \(\mathfrak{q}\) be a parabolic subalgebra. Let M be a generalized Verma module induced from a one dimensional representation of \(\mathfrak{q}\). Such M is called a scalar generalized Verma module. In this paper, we will determine the reducibility of scalar generalized Verma modules associated to maximal parabolic subalgebras by computing explicitly the Gelfand–Kirillov dimension of the corresponding highest weight modules.
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We would like to thank the anonymous referees for providing many constructive comments and help in improving the contents of our paper.
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Supported by the National Science Foundation of China (Grant No. 12171344) and the National Key R&D Program of China (Grant Nos. 2018YFA0701700 and 2018YFA0701701)
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Bai, Z.Q., Jiang, J. Gelfand–Kirillov Dimension and Reducibility of Scalar Generalized Verma Modules for Classical Lie Algebras. Acta. Math. Sin.-English Ser. 40, 658–706 (2024). https://doi.org/10.1007/s10114-024-2676-2
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DOI: https://doi.org/10.1007/s10114-024-2676-2