Bilinear Forms on Skein Modules and Steps in Dyck Paths

Details Bilinear Forms on Skein Modules and Steps in Dyck Paths Bilinear Forms on Skein Modules and Steps in Dyck Paths

2010-11-03

arxiv.org/abs/1011.0941v2

Mathematics

Quantum Algebra

Correct a mistake in Definition 6.5

Scientific paper

10.1063/1.3609231

We use Jones-Wenzl idempotents to construct bases for the relative Kauffman bracket skein module of a square with n points colored 1 and one point colored h. We consider a natural bilinear form on this skein module. We calculate the determinant of the matrix for this form with respect to the natural basis. We reduce the computation to count some steps in generalized Dyck paths. Moreover, we relate our determinant to a determinant on semi-meanders.

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