Twisted Alexander polynomial for the Lawrence-Krammer representation
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چکیده
منابع مشابه
Twisted Alexander Polynomial for the Lawrence-krammer Representation
In this paper, we prove that the twisted Alexander polynomial for the Lawrence-Krammer representation of the braid group B4 is trivial. This gives an answer for the problem whether the twisted Alexander polynomial for given faithful representations is always non-trivial.
متن کاملInvariant Subspaces of the Lawrence–krammer Representation
The Lawrence–Krammer representation was used in 2000 to show the linearity of the braid group. The problem had remained open for many years. The fact that the Lawrence–Krammer representation of the braid group is reducible for some complex values of its two parameters is now known, as well as the complete description of these values. It is also known that when the representation is reducible, t...
متن کاملThe Lawrence–krammer Representation Is Unitary
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 Lawr...
متن کاملOn the image of the Lawrence– Krammer representation
A non-singular sesquilinear form is constructed that is preserved by the Lawrence-Krammer representation. It is shown that if the polynomial variables q and t of the Lawrence-Krammer representation are chosen to be appropriate algebraically independant unit complex numbers, then the form is negativedefinite Hermitian. Since unitary matrices diagonalize, the conjugacy class of a matrix in the un...
متن کاملA note on the image of the Lawrence - Krammer representation
A non-singular sesquilinear form is constructed that is preserved by the Lawrence-Krammer representation. It is shown that if the polynomial variables q and t of the Lawrence-Krammer representation are chosen to be appropriate algebraically independant unit complex numbers, then the form is negativedefinite Hermitian. Unitary matrices diagonalize, and it is shown that the eigenvalues of a Lawre...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2004
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700035826