In this talk a “model” of a finite group or semisimple algebra means a representation containing a unique irreducible subrepresentation from each isomorphism class. In the 1980s Klyachko identified an elegant model for the general linear group over a finite field with q elements. There is an informal sense in which taking the q→1 limit of Klyachko’s construction gives a model for the symmetric group, which can be extended to its Iwahori-Hecke algebra. The resulting Hecke algebra representation is a special case of a “perfect model”, which is a more flexible construction that can be considered for any finite Coxeter group. In this talk, I will classify exactly which Coxeter groups have perfect models, and discuss some notable features of this classification. For example, each perfect model gives rise to a pair of related W-graphs, which are dual in types B and D but not in type A. Various interesting questions about these W-graphs remain open.
This is joint work with Yifeng Zhang.
This video was produced by the Okinawa Institute of Science and Technology, as part of their OIST Representation Theory Seminar series.
