Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory

Abstract

The Kronecker, plethysm and Sylow branching coefficients describe the decomposition of representations of symmetric groups obtained by tensor products and induction. Understanding these decompositions has been hailed as one of the definitive open problems in algebraic combinatorics and has profound and deep connections with representation theory, symplectic geometry, complexity theory, quantum information theory, and local-global conjectures in representation theory of finite groups. The overarching theme of the Mini-Workshop has been the use of hidden, richer representation theoretic structures to prove and disprove conjectures concerning these coefficients. These structures arise from the modular and local-global representation theory of symmetric groups, graded representation theory of Hecke and Cherednik algebras, and categorical Lie theory.