Otto-von-Guericke-Universität Magdeburg


Prof. Peter McMullen, Ph.D. D.Sc.

Realizations of symmetric sets

A symmetric set is a pair (V, G) consisting of a finite set Ʋ and a subgroup G of its permutations that acts transitively on V. A realization is a mapping (V, G) → (W, G), where G is a representation of G in the orthogonal group O(E) in some euclidean space E, and the action of G on W ⊆ E is induced by that of G on W. Different realizations of (V, G) can be combined in various geometric ways, analogous to scaling, addition and multiplication, leading to a kind of algebra of realizations. In particular, the normalized realizations (where W lies in a unit sphere) naturally form a compact convex set. An inner product on realizations yields orthogonality relations reminiscent of those for representations of groups. However, representations play only a minor part in what is a very geometric theory.

Datum: 08.04.2014, Raum: G02-311, Zeit: 17:00
Letzte Änderung: 16.11.2016 - Ansprechpartner: Prof. Dr. Volker Kaibel
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