Inner products on the Hecke algebra of the braid group
Geometric Topology
2009-07-01 v1 Representation Theory
Abstract
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.
Keywords
Cite
@article{arxiv.0906.5555,
title = {Inner products on the Hecke algebra of the braid group},
author = {Tamás Kálmán},
journal= {arXiv preprint arXiv:0906.5555},
year = {2009}
}