Knizhnik-Zamolodchikov bundles are topologically trivial

Details Knizhnik-Zamolodchikov bundles are topologically trivial Knizhnik-Zamolodchikov bundles are topologically trivial

2008-09-21

arxiv.org/abs/0809.3590v1

Mathematics

Quantum Algebra

12 pages

Scientific paper

We prove that the vector bundles at the core of the Knizhnik-Zamolodchikov and quantum constructions of braid groups representations are topologically trivial bundles. We provide partial generalizations of this result to generalized braid groups. A crucial intermediate result is that the representation ring of the symmetric group on n letters is generated by the alternating powers of its natural n-dimensional representation.

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