Representations of the Exceptional Lie Superalgebra E(3, 6) Iii: Classification of Singular Vectors
نویسندگان
چکیده
We continue the study of irreducible representations of the exceptional Lie superalgebra E(3, 6). This is one of the two simple infinite-dimensional Lie superalgebras of vector fields which have a Lie algebra sl(3) × sl(2) × gl(1) as the zero degree component of its consistent Z-grading. We provide the classification of the singular vectors in the degenerate Verma modules over E(3, 6), completing thereby the classification and construction of all irreducible E(3, 6)modules that are L0-locally finite.
منابع مشابه
A.: Representations of the exceptional Lie superalgebra E(3, 6) III: Classification of singular vectors (in preparation
Four Z+-bigraded complexes with the action of the exceptional infinitedimensional Lie superalgebra E(3, 6) are constructed. We show that all the images and cokernels and all but three kernels of the differentials are irreducible E(3, 6)-modules. This is based on the list of singular vectors and the calculation of homology of these complexes. As a result, we obtain an explicit construction of al...
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