Coincidence rotations of the root lattice A4

  • Authors:

  • Michael Baake;Uwe Grimm;Manuela Heuer;Peter Zeiner

  • Affiliations:

  • Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany;Department of Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK;Department of Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK;Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2008

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Abstract

The coincidence site lattices of the root lattice A"4 are considered, and the statistics of the corresponding coincidence rotations according to their indices is expressed in terms of a Dirichlet series generating function. This is possible via an embedding of A"4 into the icosian ring with its rich arithmetic structure, which recently [M Baake, M. Heuer, R.V. Moody, Similar sublattices of the root lattice A"4, preprint arXiv:math.MG/0702448] led to the classification of the similar sublattices of A"4.