Combinatorical and Algebraic Structures Seminar
Session details
| Date: | 4.3.2008 |
| Speaker: | Manuela Heuer, Open University, Milton Keynes, UK |
| Title: | Coincidence Rotations of the Root Lattice $\mathbf{A_4}$ |
| Abstract: | (spoluautoři: Michael Baake, Uwe Grimm and Peter Zeiner) An isometry $R$ of $\mathbb{R}^d$ is called a coincidence isometry of a lattice $\varGamma \subset \mathbb{R}^d$ if $\varGamma$ and $R \varGamma$ have a common sublattice. The intersection $\varGamma \cap R \varGamma$ is then called a coincidence site lattice of the isometry $R$.\\ The coincidence site lattices of the root lattice $A_4 \subset \mathbb{R}^4$ are considered, and it is described how an embedding of $A_4$ into the icosian ring, with its rich arithmetic structure, leads to a Dirichlet series generating function for the number of coincidence rotations of $A_4$. |
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