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Let $\mathfrak{g}$ be a simple Lie algebra over $\mathbb{C}$. The KZconnection is a connection on the constant bundle associated to a set of $n$finite dimensional irreducible representations of $\mathfrak{g}$ and a nonzero$\kappa \in \mathbb{C}$, over the configuration space of $n$-distinct points onthe affine line. Via the work of Schechtman--Varchenko and Looijenga, when$\kappa$ is a rational number the associated local systems can be seen to berealisations of naturally defined motivic local systems. We prove a basicfactorisation for the nearby cycles of these motivic local systems as some ofthe $n$ points coalesce.  This leads to the construction of a family (parametrised by $\kappa$) ofdeformations over $\mathbb{Z}[t]$ of the representation ring of$\mathfrak{g}$--we call these enriched representation rings--which allows oneto compute the ranks of the Hodge filtration of the associated variations ofmixed Hodge structure; in turn, this has applications to both the local andglobal monodromy of the KZ connection. In the case of $\mathfrak{sl}_n$ we givean explicit algorithm for computing all products in the enriched representationrings, which we use to prove that if $1/\kappa$ is an integer then the globalmonodromy is finite and scalar.  We also prove a similar factorisation result for motivic local systemsassociated to conformal blocks in genus $0$; this leads to the construction ofa family of deformations of the fusion rings. Computations in these rings havepotential applications to finiteness of global monodromy.  Several open problems and conjectures are formulated. These include questionsabout motivic BGG-type resolutions and the relationship between the Hodgefiltration and the filtration by conformal blocks at varying levels.

Motivic factorisation of KZ local systems and deformations of representation and fusion rings