From Klyachko models to perfect models

Abstract: 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 $q \to 1$ 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.

combinatoricsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

OIST representation theory seminar

Series comments: Timings of this seminar may vary from week to week.