A Gram Determinant For Lickorish's Bilinear Form

TL;DR

This paper introduces a new basis for the Temperley-Lieb algebra using Jones-Wenzl idempotents, enabling a simplified calculation of the Gram determinant for Lickorish's bilinear form.

Contribution

The authors develop a basis for TL_n with Jones-Wenzl idempotents, providing a more efficient method to compute the Gram determinant.

Findings

Simplified calculation of the Gram determinant

New basis for Temperley-Lieb algebra

Enhanced understanding of bilinear forms

Abstract

We use the Jones-Wenzl idempotents to construct a basis of Temperley-Lieb algebra TL_n. This allows a short calculation for a Gram determinant of Lickorish's bilinear form on the Temperley-Lieb algebra.