Johannes Grassberger ; Günther Hörmann - A note on representations of the finite Heisenberg group and sums of greatest common divisors

dmtcs:284 - Discrete Mathematics & Theoretical Computer Science, January 1, 2001, Vol. 4 no. 2 - https://doi.org/10.46298/dmtcs.284
A note on representations of the finite Heisenberg group and sums of greatest common divisors

Authors: Johannes Grassberger 1; Günther Hörmann 2

  • 1 Abdus Salam International Centre for Theoretical Physics [Trieste]
  • 2 Fakultät für Mathematik [Wien]

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.

https://doi.org/10.46298/dmtcs.284
Source: HAL:hal-00958949v1
Volume: Vol. 4 no. 2
Published on: January 1, 2001
Imported on: March 26, 2015
Keywords: Heisenberg group,representation of finite groups,sums of gcds,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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