Gram Determinants of Type B and Type Mb
摘要
In this lecture, we introduce the Gram determinant of the type B Temperley-Lieb algebra, where the closure is taken in the annulus. We present a proof of this formula originally given by Q. Chen and the first author and heavily influenced by the work of W. B. Raymond Lickorish on the Witten-Reshetikhin-Turaev invariant of 3-manifolds. We then discuss the Gram determinant of type Mb where the closure is taken in a Möbius band. We state some results that support the closed formula for this Gram determinant conjectured by Q. Chen in 2009.