Codes and Expansions (CodEx) Seminar

Dom Vito Briones (Nanyang Technological University)
Equiangular tight frames from fusion schemes

Iverson, Jasper, and Mixon obtained Gram matrices of equiangular tight frames (ETFs) as sums of primitive idempotents of commutative association schemes. Through this idea, they produced an infinite family of ETFs using the association schemes produced by Suzuki 2-groups.

Using the second eigenmatrix of an association scheme, we formulate a necessary and sufficient condition for a sum of primitive idempotents of the scheme to be the Gram matrix of an ETF. Applying this characterization to fusion schemes, we show that the Gram matrices of ETFs from the Suzuki 2-groups are obtained from 3-class fissions of complete multipartite graphs.