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The Lawrence--Krammer representation is unitary | | Won Taek Song
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21 Feb 2002 | | Subject: | Geometric Topology; Representation Theory MSC-class: 20F36; 57M07 | math.GT math.RT | | Abstract: | We 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. | | Source: | arXiv, math.GT/0202214 | | Services: | Forum | Review | PDF | Favorites | |
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