Abstract
In this note, we give the dimensions of some irreducible representations of exceptional Lie algebras and algebraic groups. Similar results appear in [1] for classical groups and algebras of rank at most 4. These results were produced by computer programs developed in connection with [3], where the main result required information beyond the tables in [1]. In view of the utility of the tables in [1], it seemed worthwhile to provide tables for groups of higher rank. Although our methods are similar to those of [l], they incorporate a reduction process which permits us to push the techniques a bit further.
Research partially supported by NSF grant DMS-8414528
Research partially supported by NSF grant DMS-8318037
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References
Burgoyne, N. and Williamson, C., Some computations involving simple Lie algebras, Proc. 2nd. Symp. Symbolic and Algebraic Manipulation, ed., S. P. Petrick, N.Y. Assoc. Computing Machinery, 1971.
Carter, R., Simple groups of Lie Type, Wiley, New York, 1972.
Seitz, G., The maximal subgroups of classical algebraic groups, A.M.S. Memoirs, 365 (1987) 1–286.
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© 1988 D. Reidel Publishing Company, Dordrecht, Holland
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Gilkey, P.B., Seitz, G.M. (1988). Some representations of exceptional Lie algebras. In: Aschbacher, M., Cohen, A.M., Kantor, W.M. (eds) Geometries and Groups. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4017-8_14
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DOI: https://doi.org/10.1007/978-94-009-4017-8_14
Publisher Name: Springer, Dordrecht
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