On the largest representation in type H₄

2020/03/02 by Marin, Ivan
#FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2003.00742

Abstract

In this technical note, we complete the PhD work of A. Esterle about determining the image of any Artin group of finite Coxeter type inside the associated Hecke algebra over a finite field, when the latter is semisimple. The only remaining case was the 48-dimensional irreducible representation in type H₄, for which the image is proven here to be Ω₄₈⁺.

Related

• Artin Groups and Iwahori-Hecke algebras over finite fields
• Image of the Artin groups of classical types inside the finite Iwahori-Hecke algebras
• The representation dimension of Hecke algebras and symmetric groups
• Representations of A-type Hecke algebras
• Maximal representation dimension of finite p-groups