Abstract
We present explicit formulas for α-primitive elements in the generalized Verma module, which generalize the known formulas for primitive elements in the Verma modules.
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REFERENCES
D. P. Zhelobenko, Representations of Reductive Lie Algebras [in Russian], Nauka, Moscow (1994).
J. Dixmier, Universal Enveloping Algebras [Russian translation], Mir, Moscow (1978).
V. Futorny and V. Mazorchuk, “Structure of α-stratified modules for finite-dimensional Lie algebras,” J. Algebra, 183, 456–482 (1996).
V. M. Futornyi, “A generalization of Verma modules and irreducible representations of the algebra sl (3,ℂ,” Ukr. Mat. Zh., 48, No.2, 492–497 (1991).
R. M. Asherova, Yu. F. Smirnov, and V. M. Tolstoi, “Projection operators for simple Lie groups,” Zh. Teor. Mat. Fiz., 8, No.2, 255–271 (1971).
N. Bourbaki, Lie Algebras and Lie Groups [Russian translation], Mir, Moscow (1972).
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Khomenko, O.M. α-Primitive Elements in the Generalized Verma Modules. Ukrainian Mathematical Journal 52, 1300–1306 (2000). https://doi.org/10.1023/A:1010365407300
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DOI: https://doi.org/10.1023/A:1010365407300