Quebec Mathematical Sciences Colloquium

October 30, 2014 from 16:00 to 18:00 (Montreal/Miami time) On location

A Pedestrian Approach to Group Representations

Colloquium presented by Georgia Benkart (University of Wisconsin-Madison)

Determining the number of walks of n steps from vertex A to vertex B on a graph often involves clever combinatorics or tedious treading. But if the graph is the representation graph of a group, representation theory can facilitate the counting and provide much insight. This talk will focus on connections between Schur-Weyl duality and walking on representation graphs. Examples of special interest are the simplylaced affine Dynkin diagrams, which are the representation graphs of the finite subgroups of the special unitary group SU(2) by the McKay correspondence. The duality between the SU(2) subgroups and certain algebras enables us to count walks and solve other combinatorial problems, and to obtain connections with the Temperley-Lieb algebras of statistical mechanics, with partitions, with Stirling numbers, and much more.

Address

CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, room 6214