A Pentagonal Crystal, the Golden Section, alcove packing and aperiodic tilings

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dc.creatorJoseph, Anthony
dc.date2008-11-03
dc.date.accessioned2026-07-07T10:14:55Z
dc.date.available2026-07-07T10:14:55Z
dc.descriptionA Lie theoretic interpretation is given to a pattern with five-fold symmetry occurring in aperiodic Penrose tiling based on isosceles triangles with length ratios equal to the Golden Section. Specifically a $B(\infty)$ crystal based on that of Kashiwara is constructed exhibiting this five-fold symmetry. It is shown that it can be represented as a Kashiwara $B(\infty)$ crystal in type $A_4$. Similar crystals with $(2n+1)$-fold symmetry are represented as Kashiwara crystals in type $A_{2n}$. The weight diagrams of the latter inspire higher aperiodic tiling. In another approach alcove packing is seen to give aperiodic tiling in type $A_4$. Finally $2m$-fold symmetry is related to type $B_m$.
dc.description57 pages, 12 figures
dc.identifierhttps://arxiv.org/abs/0811.0336
dc.identifierhttp://arxiv.org/abs/0811.0336
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173051
dc.subjectRepresentation Theory
dc.titleA Pentagonal Crystal, the Golden Section, alcove packing and aperiodic tilings
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