Discrete Mathematics & Theoretical Computer Science, Vol 4, No 2 (2001)

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A note on representations of the finite Heisenberg group and sums of greatest common divisors

Johannes Grassberger, Günther Hörmann


We review an elementary approach to the construction of all irreducible representations of the finite Heisenberg group. Determining the number of inequivalent classes of irreducible representations by different methods leads to an identity of sums involving greatest common divisors. We show how this identity can be generalized and derive an explicit formula for the sums.

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