Abstract
We obtain a description of all irreducible complex representations of the group indicated in the title (p ≠ 2 is a prime). Namely, for each n ≥ 2 we distinguish three series of representations of degrees (p + 1)pn−1, (p2 − 1)pn−2, (p − 1)pn−1. The other representations of\(GL(2,Z_{p^n } )\) are obtained from representations of\(GL(2,Z_{p^{n - 1} } )\) by tensor multiplication by one-dimensional representations.
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 64, pp. 95–103, 1976.
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Nagornyi, S.V. Complex representations of the group GL(2, Z/pnZ). J Math Sci 17, 1777–1783 (1981). https://doi.org/10.1007/BF01091765
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DOI: https://doi.org/10.1007/BF01091765