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  1. Home > Articles & Issues >
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  3. A note on representa ...
Article

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

Johannes Grassberger (1), Günther Hörmann (2)
(1) Abdus Salam International Centre for Theoretical Physics [Trieste]
(2) Fakultät für Mathematik [Wien]
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Imported on
March 26, 2015
Published on
January 1, 2001
Last modified on
March 31, 2025
Volume 4
vol. 4:2
DOI
10.46298/dmtcs.284
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https://about.hal.science/hal-authorisation-v1
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A note on representations of the finite Heisenberg group and sums of greatest common divisors

Johannes Grassberger (1), Günther Hörmann (2)
(1) Abdus Salam International Centre for Theoretical Physics [Trieste]
(2) Fakultät für Mathematik [Wien]
Abstract
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.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • Heisenberg group
  • representation of finite groups
  • sums of gcds
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