
doi: 10.1007/bf02577133
In almost all problems in the representation theory of reductive Lie algebras one meets extremal equations (that is, equations in the ``highest vector''). In this article we consider extremal equations in a wide class of modules similar to the ``universal modules'' of Verma. A wider program of the study of such equations and related objects (Mickelsson algebras, Verma modules, etc.) has been given earlier by the author. The results of the present article were reported briefly in [Funct. Anal. Appl. 19, 325-327 (1985); translation from Funkts. Anal. Prilozh. 19, No.4, 88-89 (1985; Zbl 0593.17007)].
complex Lie algebra, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), extremal projections, extremal equations, enveloping algebra, Verma modules, root system, reductive Lie algebras, Universal enveloping (super)algebras, Simple, semisimple, reductive (super)algebras
complex Lie algebra, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), extremal projections, extremal equations, enveloping algebra, Verma modules, root system, reductive Lie algebras, Universal enveloping (super)algebras, Simple, semisimple, reductive (super)algebras
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