Monday, April 14, 2014
Freie Universität Berlin
Institut für Informatik
Takustr. 9
14195 Berlin
room 005
Lecture - 14:15
Abstract:
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.