Vector Delannoy Categories and Further Developments

Explore a comprehensive lecture on Vector Delannoy categories and their quantum analogues presented by Sophie Kriz from Princeton University at IPAM's Symmetric Tensor Categories and Representation Theory Workshop. Delve into the construction of "quantum" or "q-1" analogues of the Delannoy category, focusing on the use of relative measures on oligomorphic groups. Examine the "Borel" case involving linear transformations of free vector spaces over finite fields, and discover the unipotent version proposed by P. Deligne. Investigate the properties of these categories, including simple objects and their connection to the original Delannoy category. Gain insights into Kriz's formalism of "T-algebras" and its role in discovering the Borel q-1 Delannoy category. Enhance your understanding of advanced topics in representation theory and category theory through this in-depth 54-minute presentation recorded on January 10, 2024, at the Institute for Pure & Applied Mathematics (IPAM) at UCLA.