The Delannoy Category - Symmetric Tensor Categories and Representation Theory

Explore a 52-minute lecture on "The Delannoy Category" presented by Noah Snyder from Indiana University at IPAM's Symmetric Tensor Categories and Representation Theory Workshop. Delve into the theory of pre-Tannakian categories derived from oligomorphic permutation groups and their associated G-set measures. Examine Deligne's S_t as a prototype and discover a new example based on order-preserving bijections of the real line. Uncover the detailed description of this novel symmetric tensor category, including the classification of simple objects, tensor product rules, and a combinatorial model using Delannoy paths. Gain insights into the category's unique properties and dimensions of Hom spaces related to Delannoy numbers. Conclude with a brief introduction to the non-semisimple "circular Delannoy category" arising from order-preserving bijections of the circle.