Representation Theory and Algebraic Combinatorics Unit (Liron Speyer)
The Representation Theory and Algebraic Combinatorics Unit is interested in the study of the representation theory of many (usually finite-dimensional) algebras relating to symmetric groups. These include many famous examples, including the deformations known as Iwahori–Hecke algebras, their generalisations to deformations of complex reflection groups (the cyclotomic Hecke algebras), their quasi-hereditary covers (cyclotomic q-Schur algebras and Cherednik algebras), quiver Hecke algebras, and many other related diagram algebras. The common ground shared by these algebras is a powerful combinatorial framework that governs their representation theory, such as (multi)partitions and standard tableaux, often also giving these algebras a so-called cellular structure.
We are especially interested in making progress on the decomposition number problem, that seeks to understand the simple constituents of the ordinary irreducible modules in the modular case, as well as other problems that fit into the framework of 'decomposing representations'.