Bose-Mesner algebra and subconstituent algebra of an association scheme,   Sung Y. Song,   Iowa State University,  Wed, 9 September, 2009,   3:00 p.m. C-209


We will discuss an algebraic approach to the characterization problem for an association scheme. We survey properties of the Bose-Mesner algebra and the subconstituent algebra of a metric scheme in algebraic combinatorics, an area that includes theory of association schemes, algebraic graph theory, coding theory, group representation theory, design theory, among others. The main topics discussed include the following:
  1. The connection between distance-regular graphs and association schemes.
  2. Bose-Mesner algebras of graphs and association schemes.
  3. Subconstituent algebras of association schemes.
(This talk is aimed at non-specialists in algebraic combinatorics, so some material which is well-known to the experts in algebraic combinatorics is included in here.