Lawrence-Krammer-Paris representations under graph automorphisms.

Anatole Castella (1)

1 ICJ - Institut Camille Jordan

Lawrence-Krammer-Paris representations (LKP for short) are the first examples of faithful linear representations of the Artin-Tits monoids of small type (and hence of the Artin-Tits groups of spherical and small type). If the construction is essentially unique for the spherical and small types, the same is not clear for a spherical and non-small type. Another important open question is to ask if there exists an analogue of this construction for the non-small types. The aim of this paper is to classify all the LKP-representations for the {\it affine} and small types, and to generalize the construction of [Digne, \emph{On the linearity of Artin Braid groups.} J. Algebra \textbf{268}, (2003) 39-57] in order to provide ``LKP-like'' faithful linear representations of any Artin-Tits monoid that appears as the submonoid of fixed points of an Artin-Tits monoid of small type under the action of graph automorphisms.

Domaines: Théorie des groupes [math.GR]

Anatole Castella. Lawrence-Krammer-Paris representations under graph automorphisms.. 2008. ⟨hal-00261496v1⟩