The Lawrence--Krammer representation is unitary

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dc.creatorSong, Won Taek
dc.date2002-02-21
dc.date.accessioned2026-07-07T04:46:36Z
dc.date.available2026-07-07T04:46:36Z
dc.descriptionWe show that the Lawrence--Krammer representation is unitary. We explicitly present the non-singular matrix representing the sesquilinear pairing invariant under the action. We show that reversing the orientation of a braid is equivalent to the transposition of its Lawrence--Krammer matrix followed by a certain conjugation. As corollaries it is shown that the characteristic polynomial of the Lawrence--Krammer matrix is invariant under substitution of its variables with their inverses up to multiplication by units, and is not a complete conjugacy invariant for braids.
dc.description16 pages, 53 pictures
dc.identifierhttps://arxiv.org/abs/math/0202214
dc.identifierhttp://arxiv.org/abs/math/0202214
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63395
dc.subjectGeometric Topology
dc.subjectRepresentation Theory
dc.subject20F36; 57M07
dc.titleThe Lawrence--Krammer representation is unitary
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