A Quaternionic Braid Representation (after Goldschmidt and Jones)
نویسنده
چکیده
We show that the braid group representations associated with the (3, 6)-quotients of the Hecke algebras factor over a finite group. This was known to experts going back to the 1980s, but a proof has never appeared in print. Our proof uses an unpublished quaternionic representation of the braid group due to Goldschmidt and Jones. Possible topological and categorical generalizations are discussed.
منابع مشابه
Unitary braid representations with finite image
In this paper, we prove two loosely connected results about unitary representations of the braid group W Bn!U.d/, when n is sufficiently large and the degree d is not too large compared to n. The original motivation goes back to the work of Jones on images of Braid groups in Hecke algebra representations H.q; n/. Jones showed [10] that when q D i , the image of Bn in every irreducible factor of...
متن کاملThe Two-Eigenvalue Problem and Density of Jones Representation of Braid Groups
1. The Two-Eigenvalue Problem . . . . . . . . . . . . . . . . . . . . . . . . 179 2. Hecke Algebra Representations of Braid Groups . . . . . . . . . . . . . . 183 3. Duality of Jones–Wenzl Representations . . . . . . . . . . . . . . . . . . 186 4. Closed Images of Jones–Wenzl Sectors . . . . . . . . . . . . . . . . . . . 188 5. Distribution of Evaluations of Jones Polynomials . . . . . . . . . ...
متن کاملDoes the Jones Polynomial Detect the Unknot?
We address the question: Does there exist a non-trivial knot with a trivial Jones polynomial? To find such a knot, it is almost certainly sufficient to find a non-trivial braid on four strands in the kernel of the Burau representation. I will describe a computer algorithm to search for such a braid.
متن کاملProperties of Closed 3-braids and Other Link Braid Representations
We show that 3-braid links with given (non-zero) Alexander or Jones polynomial are finitely many, and can be effectively determined. We classify among closed 3-braids strongly quasi-positive and fibered ones, and show that 3-braid links have a unique incompressible Seifert surface. We also classify the positive braid words with Morton-Williams-Franks bound 3 and show that closed positive braids...
متن کاملBraids, the Artin Group, and the Jones Polynomial
This paper is about Braids and the Artin braid group Bn. After some initial definitions and examples, I proceed to show how the Jones polynomial can be derived through a representation of the braid group by the Temperley-Lieb Algebra, an approach similar to Jones’ original construction. 1 Braids, An Introduction Perhaps the most obvious place to start is with the definition [3] of a braid: Defi...
متن کامل