Nikolaus conference 2016

Speaker: Alexandre Esterle (Amiens)

Title: Image of the Artin Groups of Type A and B Inside the Finite Hecke Algebras

Abstract:

In his doctoral thesis, Hoefsmit gave matrix models defined over the ring of Laurent polynomials over rational numbers for the Hecke Algebras of types A,B and D. Given certain conditions, those models can be defined over a finite field. I. Marin determined in the generic case the Zariski closure of the Artin groups of all types inside the Hecke Algebra. O. Brunat, K.Magaard and I.Marin then determined the image of the braid group inside the Hecke Algebra of type A defined over a finite field. In this talk, we will first give the general idea of how the image was obtained in type A and then give the result obtained in type B.

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