Combinatorics of Principal W-algebras of Type A

Watch a 44-minute mathematics lecture from the Workshop on Representation Theory, Calabi-Yau Manifolds, and Mirror Symmetry where Dr. Shashank Kanade from the University of Denver explores the combinatorial aspects of principal W-algebras of type A. Discover how cylindric partitions control the combinatorics of principal W_r(p,p') algebras, with particular focus on Welsh's work on Virasoro minimal models and the A_2 Bailey machinery developed by Andrews, Schilling and Warnaar. Learn about recent conjectures developed with Russell regarding W_3(3,p') modules and their proofs for small p' values. Examine the connection between W_r(p,p') algebra characters and sl_r colored Jones invariants of torus knots T(p,p'), understanding their potential implications for combinatorial insights.