This 10-day workshop is devoted to the representation theory of symmetric groups and related algebras.
The representation theory of symmetric groups and related algebras is a vibrant and dynamic research area. The rich structure enjoyed by the symmetric group algebras, with combinatorics playing a significant role, enables it to be studied as specific examples in the modular representation theory of finite groups, and as algebras of wild representation type. Some of its naturally occurring representations (such as the Lie modules) also have surprising links with other branches of mathematics (such as algebraic topology).
Despite its rich structure, symmetric group algebras are still not well understood, and many problems—some of them fundamental—remain open. The most famous among these is probably the complete determination of its decomposition numbers. The recent advent of Khovanov-Lauda-Rouquier (KLR) algebras provides a breakthrough in their understanding, tying the quantized decomposition numbers arising from the canonical basis of the Fock space representation of the quantum affine special linear Lie algebra to the graded decomposition numbers of symmetric groups. On the other hand, the recent announcement by Williamson of counter-examples to James’s conjecture ensures that these decomposition numbers remain as mysterious as ever.
The workshop aims to survey the recent development and provide impetus for further insights and progress. It hopes to bring together researchers working in this area to foster interaction, collaboration and the exchange of ideas.