On monomial representations of finitely generated nilpotent groups |
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Authors: | E. K. Narayanan |
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Affiliation: | Department of Mathematics, Indian Institute of Science, Bangalore, India |
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Abstract: | A result of Segal states that every complex irreducible representation of a finitely generated nilpotent group G is monomial if and only if G is abelian-by-finite. A conjecture of Parshin, recently proved affirmatively by Beloshapka and Gorchinskii (2016), characterizes the monomial irreducible representations of finitely generated nilpotent groups. This article gives a slightly shorter proof of the conjecture using ideas of Kutzko and Brown. We also give a characterization of the finite-dimensional irreducible representations of two-step nilpotent groups and describe these completely for two-step groups whose center has rank one. |
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Keywords: | Discrete Heisenberg groups finitely generated nilpotent groups induced representations monomial representations |
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