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Complex representations of the full linear group over a finite field

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Abstract

The properties of the system of irreducible complex representations of full linear groups are described, without making use of the characteristics of the representations. The description is given in terms involving the multiplication of irreducible representations, which was introduced by Green. Explicitly, the concept of prime and primary representations is introduced, theorems are proved on the unique decomposition into primary factors, and the structure of the primary representations, belonging to a fixed prime representation, is described.

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Authors
  1. D. K. Faddeev
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskoto Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 46, pp. 64–88, 1974.

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Faddeev, D.K. Complex representations of the full linear group over a finite field. J Math Sci 9, 341–363 (1978). https://doi.org/10.1007/BF01085053

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  • DOI: https://doi.org/10.1007/BF01085053

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