Graduiertenkolleg: Methods for Discrete Structures

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Monday Lecture and Colloquium

Monday, April 14, 2014

Freie Universität Berlin
Institut für Informatik
Takustr. 9
14195 Berlin
room 005

Lecture - 14:15

Peter McMullen - University College London

Realizations of symmetric sets

- - - Handout - - -

A symmetric set is a pair (V, G) consisting of a finite set V and a subgroup G of its permutations that acts transitively on V. A realization is a mapping (V, G) → (V, 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 V ⊆ 𝔼 is induced by that of G on V . 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 V 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.


Letzte Aktualisierung: 15.04.2014