Inner products on the Hecke algebra of the braid group

Details Inner products on the Hecke algebra of the braid group Inner products on the Hecke algebra of the braid group

2009-06-30

arxiv.org/abs/0906.5555v1

Mathematics

Geometric Topology

Scientific paper

We point out that the Homfly polynomial (that is to say, Ocneanu's trace functional) contains two polynomial-valued inner products on the Hecke algebra representation of Artin's braid group. These bear a close connection to the Morton-Franks-Williams inequality. In these structures, the sets of positive, respectively negative permutation braids become orthonormal bases. In the second case, many inner products can be geometrically interpreted through Legendrian fronts and rulings.

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