Abstract

Extending representation theory from finite groups to finite semigroups brings interesting challenges, combinatorics, and applications. Almost a decade ago, I proposed an algorithm to compute the Cartan Matrix of a semigroup algebra—a combinatorial invariant that contains information on how projective modules are built from simple modules. It boils down to computing with finite semigroups, characters of groups, and combinatorics. Despite this relative simplicity, and much to my embarrassment, a full production-grade implementation is only finally in reach.  

In this talk, I will report on ongoing joint work with my PhD student Balthazar Charles to implement this algorithm and adapt it to modular representations, and use this occasion to illustrate the evolution of our computational landscape toward an ecosystem of interoperable software, thanks to large scale collaborations.