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A simple proof of the faithfulness of the Lawrence-Krammer-Paris representation. (Une démonstration simple de la fidélité de la représentation de Lawrence-Krammer-Paris.) (French) Zbl 1163.20025
Summary: The theorem of linearity of the Artin-Tits groups of spherical type and the theorem of injectivity of any Artin-Tits monoid in its group are essentially based on the faithfulness of the Lawrence-Krammer-Paris representation restricted to the monoid. We prove this faithfulness using neither the normal forms of the elements of the monoid nor the closed subsets of the associated root system; only very elementary notions are needed.

MSC:
20F36 Braid groups; Artin groups
20C15 Ordinary representations and characters
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